• Your script check equality of passwords, not username password pairs.
• If the given password doesn't match the password in the first line then it dies

Your loop needs to be more like

while ( my $line = <$fh> ) {
    chomp $line;
    my ( $name, $passwd ) = split /:/, $line;
    next unless $name eq $userName;
    ....
}
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You mak also want to look at Term::ReadKey or IO::Prompt for the password prompt