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// user fill all fields as it should, so form can be submitted
conForm.submit(function(e){ 
 var isValidForm = true;
 // prevent user from hitting submit button with empty form.
 var tempval = document.getElementById('fullname').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#fullname').addClass('bordered2'); 
 jQuery('#fullname').removeClass('good_input'); 
 jQuery("#fullname").attr("placeholder", "Εισάγετε το όνομα σας").placeholder();
 isValidForm = false;
 }
 var sEmail = jQuery('#customeremail').val();
 if (jQuery.trim(sEmail).length == 0) {
 // if user leave the field empty 
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 jQuery("#customeremail").attr("placeholder", "Εισάγετε το email σας").placeholder();
 isValidForm = false;
 }
 if (validateEmail(sEmail)) {
 // if the e-mail is valid
 jQuery('#customeremail').removeClass('bordered2'); 
 jQuery('#customeremail').addClass('good_input'); 
 } else {
 // if the e-mail is NOT valid
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 sEmail = "";
 jQuery("#customeremail").val(sEmail);
 jQuery("#customeremail").attr("placeholder", "Εισάγετε υπαρκτό email").placeholder();
 isValidForm = false;
 }
 var tempval = document.getElementById('phone').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#phone').addClass('bordered2'); 
 jQuery('#phone').removeClass('good_input'); 
 jQuery("#phone").attr("placeholder", "Εισάγετε το τηλέφωνο σας").placeholder();
 isValidForm = false;
 }
 return isValidForm; 
})

// user fill all fields as it should, so form can be submitted
conForm.submit(function(e){ 
 var isValidForm = true;
 // prevent user from hitting submit button with empty form.
 var tempval = document.getElementById('fullname').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#fullname').addClass('bordered2'); 
 jQuery('#fullname').removeClass('good_input'); 
 jQuery("#fullname").attr("placeholder", "Εισάγετε το όνομα σας");
 isValidForm = false;
 }
 var sEmail = jQuery('#customeremail').val();
 if (jQuery.trim(sEmail).length == 0) {
 // if user leave the field empty 
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 jQuery("#customeremail").attr("placeholder", "Εισάγετε το email σας");
 isValidForm = false;
 }
 if (validateEmail(sEmail)) {
 // if the e-mail is valid
 jQuery('#customeremail').removeClass('bordered2'); 
 jQuery('#customeremail').addClass('good_input'); 
 } else {
 // if the e-mail is NOT valid
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 sEmail = "";
 jQuery("#customeremail").val(sEmail);
 jQuery("#customeremail").attr("placeholder", "Εισάγετε υπαρκτό email");
 isValidForm = false;
 }
 var tempval = document.getElementById('phone').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#phone').addClass('bordered2'); 
 jQuery('#phone').removeClass('good_input'); 
 jQuery("#phone").attr("placeholder", "Εισάγετε το τηλέφωνο σας");
 isValidForm = false;
 }
 return isValidForm; 
})

UPDATE: Removed the .placeholder() code that was breaking the logic.

// user fill all fields as it should, so form can be submitted conForm.submit(function(e){

 var isValidForm = true;
 // prevent user from hitting submit button with empty form.
 var tempval = document.getElementById('fullname').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#fullname').addClass('bordered2'); 
 jQuery('#fullname').removeClass('good_input'); 
 jQuery("#fullname").attr("placeholder", "Εισάγετε το όνομα σας").placeholder();
 isValidForm = false;
 }
 var sEmail = jQuery('#customeremail').val();
 if (jQuery.trim(sEmail).length == 0) {
 // if user leave the field empty 
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 jQuery("#customeremail").attr("placeholder", "Εισάγετε το email σας").placeholder();
 isValidForm = false;
 }
 if (validateEmail(sEmail)) {
 // if the e-mail is valid
 jQuery('#customeremail').removeClass('bordered2'); 
 jQuery('#customeremail').addClass('good_input'); 
 } else {
 // if the e-mail is NOT valid
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 sEmail = "";
 jQuery("#customeremail").val(sEmail);
 jQuery("#customeremail").attr("placeholder", "Εισάγετε υπαρκτό email").placeholder();
 isValidForm = false;
 }
 var tempval = document.getElementById('phone').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#phone').addClass('bordered2'); 
 jQuery('#phone').removeClass('good_input'); 
 jQuery("#phone").attr("placeholder", "Εισάγετε το τηλέφωνο σας").placeholder();
 isValidForm = false;
 }
return isValidForm; 
})

// user fill all fields as it should, so form can be submitted
conForm.submit(function(e){  var isValidForm = true;
 // prevent user from hitting submit button with empty form.
 var tempval = document.getElementById('fullname').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#fullname').addClass('bordered2'); 
 jQuery('#fullname').removeClass('good_input'); 
 jQuery("#fullname").attr("placeholder", "Εισάγετε το όνομα σας").placeholder();
 isValidForm = false;
 }
 var sEmail = jQuery('#customeremail').val();
 if (jQuery.trim(sEmail).length == 0) {
 // if user leave the field empty 
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 jQuery("#customeremail").attr("placeholder", "Εισάγετε το email σας").placeholder();
 isValidForm = false;
 }
 if (validateEmail(sEmail)) {
 // if the e-mail is valid
 jQuery('#customeremail').removeClass('bordered2'); 
 jQuery('#customeremail').addClass('good_input'); 
 } else {
 // if the e-mail is NOT valid
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 sEmail = "";
 jQuery("#customeremail").val(sEmail);
 jQuery("#customeremail").attr("placeholder", "Εισάγετε υπαρκτό email").placeholder();
 isValidForm = false;
 }
 var tempval = document.getElementById('phone').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#phone').addClass('bordered2'); 
 jQuery('#phone').removeClass('good_input'); 
 jQuery("#phone").attr("placeholder", "Εισάγετε το τηλέφωνο σας").placeholder();
 isValidForm = false;
 }
return isValidForm; 
})

I'd remove the first instance of e.preventDefault(); and introduce a validation flag that defaults to true. Replace all of the other instances of e.preventDefault(); with a line that sets the flag to false and then return the flag at the end of the code.

Like this:

// user fill all fields as it should, so form can be submitted conForm.submit(function(e){

 var isValidForm = true;
 // prevent user from hitting submit button with empty form.
 var tempval = document.getElementById('fullname').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#fullname').addClass('bordered2'); 
 jQuery('#fullname').removeClass('good_input'); 
 jQuery("#fullname").attr("placeholder", "Εισάγετε το όνομα σας").placeholder();
 isValidForm = false;
 }
 var sEmail = jQuery('#customeremail').val();
 if (jQuery.trim(sEmail).length == 0) {
 // if user leave the field empty 
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 jQuery("#customeremail").attr("placeholder", "Εισάγετε το email σας").placeholder();
 isValidForm = false;
 }
 if (validateEmail(sEmail)) {
 // if the e-mail is valid
 jQuery('#customeremail').removeClass('bordered2'); 
 jQuery('#customeremail').addClass('good_input'); 
 } else {
 // if the e-mail is NOT valid
 jQuery('#customeremail').removeClass('good_input'); 
 jQuery('#customeremail').addClass('bordered2'); 
 sEmail = "";
 jQuery("#customeremail").val(sEmail);
 jQuery("#customeremail").attr("placeholder", "Εισάγετε υπαρκτό email").placeholder();
 isValidForm = false;
 }
 var tempval = document.getElementById('phone').value;
 if(tempval.length ==0){
 //jQuery('#p_username').focus();
 jQuery('#phone').addClass('bordered2'); 
 jQuery('#phone').removeClass('good_input'); 
 jQuery("#phone").attr("placeholder", "Εισάγετε το τηλέφωνο σας").placeholder();
 isValidForm = false;
 }
return isValidForm; 
})