Before returning it I'd try cleaning the game first if you haven't already tried that. It may look worn down but sometimes cleaning the game will really make those contacts shine. Looks can be deceiving, I thought my Mario 2 copy was shot but it worked. Also did you ever manage to fix the system, or was that ever really a problem?
I got the system working and all my games work except for Zelda and Dragon Warrior. I've cleaned those games many times, yet it seems that each time, a noticeable bit of dirt or grime is on the q-tip. I think I've cleaned those games five times or so.
The guy at the pawn shop cleaned Dragon Warrior with Windex, which was random, and even though I had bought the game three days prior, he said I was "way out of the return policy" and that I should have brought it in sooner. (even when I told him that I didn't have a working NES when I bought the game, he still didn't budge and even let me trade the game for a different one). He was an ass, but I can still try working on the game some.
If you're asking for game recommendations I've got quite a few. The Mario series is a fairly obvious choice. There are more so I made a list of my recommendations:
Gradius (good shoot em up)
Metroid or Kid Icarus
Lifeforce (another good shooter)
Duck hunt (usually comes with Mario, one of those games that's better with friends)
probably a bunch more I missed
I would get Duck Hunt, but I don't think it would work on my TV, so even though I want it, I think I'm gonna pass on it. One of the Mario games is definitively on my wish list. Thanks for the list!