You create a gamertag anyway, even if you don't have Live.
The files you transferred are, presumably, attached to what ever non-Live tag you created on the old xbox to play them.
I recently transfered all my files from White to Slim and never had a problem with the saves being allocated to the wrong tags or not being recognised. Check your old xbox for the account you created there, assuming you want to begin playing on Live with those saves means you may need to buy Live again for that gamertag.