Rather than searching the list of files, you could just check if the file exists. This approach would eliminate a lot of testing and guessing.

#!/usr/bin/perl -w
use strict;

my $path = '/Users/johnsmith/data';
my $fname;

{
    print "Please enter a filename: ";
    chomp($fname = <STDIN>);
    last if -f "$path/$fname";
    print "File does not exist!\n";
    redo;
}
print "I have found '$fname' in '$path'.\n";
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Note: Just in case you aren't trying to play guessing games with the user, you might want to consider displaying the list of available filenames. Reading up on globbing with the '<*.c>' operator or the glob operator itself should prove useful for that.