You're overwriting the hash each line of the file. You're opening files without checking the return code. You're reading the file rather oddly.

You should be using a DBM file for this. This is what DBM files were designed for. Take a look at perltie and dbmopen. I don't know what DBM libraries you have installed, but you'll definitely have at least SDBM_File, because it comes with Perl. If you have DB_File, use that.

If you're insistent on storing this in a file, try this code:

    my $FILE = "joe.txt";

    open FH, $FILE or die "Can't open $FILE: $!";
    my %hash;
    while (<FH>) {
        chomp;
        my($key, $val) = split /=>/;
        $hash{$key} = $val;
    }
    close FH or die "Can't close $FILE: $!";

    $myhash{$timestamp}=$newLine;

    open FH, ">" . $FILE or die "Can't open $FILE: $!";
    print FH join("\n", map $_ . "=>" . $hash{$_}, keys %hash), "\n";
    close FH or die "Can't close $FILE: $!";
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