Hello Palimpsest,
Unfortunately basic members only have access to the last 30 days of Games Archive (details here on the Membership page http://www.chess.com/membership.html), so if the game your interested in is any older than you will not be able to retrieve it.
Hopefully I've got that right, otherwise someone will be sure to correct me.
I played a game some time ago which I thought contained an interesting set of moves and was under the impression that your previous games are saved so you can inspect them subsequently. Is that the case or not?