Zelda and Dragon Warrior both have battery backups. I'm not terribly knowledgeable in this area, but it's possible the lithium batteries have died. There are online tutorials on how to replace the batteries; doing it is above my payscale.

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?

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:

Megaman series
Zelda series
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)
Contra
Punch out
Castlevania series
bomberman
tetris
probably a bunch more I missed

Try geting a new pin connector for the inside of your NES or get one of those reproduction NES systems like I have. The early NES systems where not built right when they where first released or something like that... try getting a new 72 pin connector and see if that will help in making your games work.

The toploader NES doesn't have the pin connector problem but pretty much any standard NES is susceptible to that problem. The main reason is Nintendo likely cheeped out and used a cheaper part for the pin connector. I would get a toploader but it doesn't have AV output, and it's more expensive.

The reason that the regular front-loading NES has pin connector issues is because of the way the system is made. Having to push down the games for them to come in full contact with the pins. If you've replaced the pin connector and some games don't work, that simply means something's wrong with the cartridge. The save battery going bad wouldn't cause the games to not work. These games are 25+ years old, so it's to be expected that some won't work. Fortunately for you, Zelda and especially Dragon Warrior are pretty cheap.

Also I apologize for not getting back to you sooner, I've been very busy. And, if you're looking to get into NES gaming, shoot me a PM.

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.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!

Sounds like your NES cartridge slot is dirty, and that's transferring the dirt to your cartridges each time you put them in there to play. I bought a refurbished Famicom recently that looked great, except the seller lied about cleaning the cartridge slot, as it transferred all kinds of nasty gunk onto my pristine Famicom carts that I'd thoroughly cleaned when I tried to play them. Once I cleaned the Famicom's cartridge slot and then cleaned my games again, it finally worked like it should have.

Anyway, that's just a thought on why your carts are constantly getting dirty.

I think he already changed the NES pin connector, but correct me if I'm wrong. If it is the game you sometimes need to scrub fairly hard to get all the grime and dirt off a game. Rubbing alcohol makes for the best cleaner, I know the warning label says not to but there is no harm in doing it. Glad to know the system works though. If it is that the cartridge slot is dirty there are cleaning kits out there that you insert like a game. I've never needed to use a cleaning kit so I can't vouch for how well they do or don't work.