There were a few issues in your code. I fixed them below.

my $sth = $dbh->prepare("INSERT INTO HLDdata (Data) VALUES (?)");
my $count = $dbh->prepare( "select count(*) from HLDdata where Data = 
+?");
foreach $txt (@TXT) {
    print "$txt\n";
    open(IN,"$txt") || warn("cant open $txt");
    while(<IN>){
        $line = $_;
        $count->execute($line);
        my ($data) = $count->fetchrow();
        print "$data \n";

        if ($data != 0){
            print "record exist not adding\n";
            Logit("record exist not adding");
            next;
        }

        my ($Data) = $line;
        $sth->execute($Data);
        $line =~s/\|/\t/g;
        # print "$line\n";
        print OUT $line;
    }
}
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Yes, you're probably correct that the checking is taking the most of the time. This is because you're missing an index on HLDdata (data) -- sqlite has to scan the whole table every time you check for a row's existence. You can create the missing index with CREATE UNIQUE INDEX HLDdata_uniq ON HLDdata (Data);

There's a trade-off: you'll now use double the disk space. If $Data tends to be big (above a hundred bytes or so), you are better off storing a hash (sha1, md5, or similar) of $Data in the table in a second column and checking for its existence instead. (SQLite does not appear to have support for functional indices or a hashing function, so you'll have to do it on the Perl side.)