You have some scoping issues. In your if blocks, you declare $FilmName and $Price with my. That makes each scoped to that block only. When you refer to $FilmName and $Price later, they will be different global varibles. Because you haven't declared them and are using strict, your script will die with a message like:

Global symbol "$FilmName" requires explicit package name at FILE line 
+LINE
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I'm guessing you haven't checked your error log. (Update: or this isn't actually very close to the actual code you are using.)

I also notice here:

my $sth = $dbh->do(
"INSERT INTO tblFilm (Name, Price) VALUES ('$FilmName', '$Price')") ||
+ print "Can't prepare statement: $DBI::errstr";
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that you probably want to use "or" instead of "||". Since || has higher precedence than =, the way it is will assign the return value of do() to $sth, or assign 1 (the return value of print) if do() returned false. With or instead of ||, $sth will be left undefined if the do() fails.