This should be enough of the code to let you see the complete picture. Hopefully I didn't miss anything important.

#!perl.exe

use strict;
use warnings;
use CGI qw(:standard -no_xhtml);

# the check_name, etc, functions are in this require'd file except in
# this example code
# require "D:/Inetpub/wwwroot/gpa/functions.pl";

my @errors;
my %app;
$app{"first_name"}      =  param('first_name');
$app{"telephone"}       =  param('telephone');
$app{"email"}           =  param('email');

# Verify the POST data (if any) using custom tests and undef bad
# values. If everything checks OK, accept the data and print a
# success message. Else print the application form (which will
# preserve all good values which users will appreciate.

if (request_method() eq "POST") {
    my $first_name_check = &check_name($app{"first_name"});
    unless ($first_name_check == "1") {
        undef $app{"first_name"};
        push (@errors, "First Name: ".$first_name_check);
    }
    my $phone_check = &check_phone($app{"telephone"});
    unless ($phone_check == "1") {
        undef $app{"telephone"};
        push (@errors, "Telephone: ".$phone_check);
    }
    my $email_check = &check_email($app{"email"});
    unless ($email_check == "1") {
        undef $app{"email"};
        push (@errors, "E-mail: ".$email_check);
    }
    if (@errors) {
        # Give the user another chance.
        &print_application;
    } else {
        # Done!
        &print_accepted;
    }
} else {
    # Give the user an application form.
    &print_application;
}

# We want first and last names to be a certain way.
sub check_name {
    my $name = $_[0];
    if ($name =~ /^[A-Z][A-Za-z\-']{2,40}/s) {
        return 1;
    } else {
        return "Helpful message.";
    }
}

# Chopped other subs to shorten post
sub check_phone {
    return 1;
}

sub check_email {
    return 1;
}


# Print account application page.
sub print_application {
    # chopped lots of non-relevant code...
    # here's those helpful error messages regarding BAD data...
    if (@errors) {
        print   h2("Account Application Error"), "\n\n",
                p(b("Problems found...")), "\n\n",
                ol(li[@errors]), "\n\n";
    }
    # print the form and populate form with GOOD data...
    # Avoiding line wraps in on-line post. n/b the funny indents :-)
    Tr(
        [
            td([
b('First Name:'),
textfield(-name=>'first_name', -default=>"$app{'first_name'}")
            ]),
            td([
b('Organization:'),
textfield(-name=>'organization', -default=>"$app{'organization'}")
            ]),
            td([
b('Telephone:'),
textfield(-name=>'telephone', -default=>"$app{'telephone'}")
            ]),
            td([
b('E-mail:'),
textfield(-name=>'email', -default=>"$app{'email'}")
            ]),
            td([
                '',
                submit
            ])
        ]
    )
}

# Print account accepted page.
sub print_accepted {
    # ...
}
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