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You'll have to change several of the .php files. I quickly glanced at index.php, adslist.php and ./blocks/catads_new.phpm all of them will need to be modified - and I'm sure there's others...
You're looking for something like:
$criteria->add(new Criteria('expired', time(),'>'));
This puts a 'qualifier' on the SQL query to exclude things that are expired (e.g. expired time before now). You can just comment out the line in most cases and then it should give you the desired results.