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hmmm....replayability is the key. and it can't be incredibly frustrating, you're already on a desert island for gods sake.

Shining Force - I love this game and even though 2 and 3 are bit more complete, the first one is a blast in my opinion. Plus it has more memorible boss battles. You can fight the battles over and over again and try out a number of strategies.

Castlevania SOTN - honestly i can just roam around this game and hack up enemies and try to collect all the "secret" items for hours. Plus once you're done...give it a shot with Richter. Good stuff.

Final Fantasy III - such an amazing game. I would play through using several different parties. Plus maybe I could finally conquer the collesium and learn all rage attacks!

Intellegent Cube - my favorite puzzle game. super addictive and fun. Challanging but not super frustrating. endless fun.

now....i need a shump. and it's a tough choice....but I'll have to go with
MUSHA - just a great game that is soo much fun to play. Awesome power-up's and bosses. i could/have played this game for hours and not once feel bored.

Runner Ups:
Dragon Force
Valkyrie Profile
Thunderforce III
R-Type III
DoDonpachi
Icaruga

No rock band for me, but at least no one said guitar hero. On Rock Band you can actually change up instruments. eventually you may get so good you can do all them instruments at once. then if/when you are finally discovered you'll be some sort of prodigy.

Because I'm bored I have narrowed it down to games beggining with S

Sonic 3 & Knuckles
Soulcalibur II
Street Fighter III 3rd Strike
Suikoden
Super Metroid

Well.... since I will be stuck there I'm going to need some long RPG's.
Persona 3 FES (for the additional 30 hours)
Persona 4
Shenmue
Shenmue II
Need for Speed Most Wanted

Hm... Tough to decide, but easier than just picking one game, because I know one game couldn't keep me occupied for long if it's all I play.
Probably something like...
Rez, because it's a good score-based game, and I've already determined I won't bore of it easily; I've played through it so many times.
Fire 'N Ice or whatever that NES puzzle game was. Because a good puzzle game is practically required.
Team Fortress 2 (this is assuming said desert has internet access.), because after quite some time I'm still not bored of it. Plus after all that time on the island I'd probably end up being a godly Spy.
Sonic and Knuckles 3 or SMB3 (can't really pick one or the other, so I'd just leave it up to a coin-toss).

Annnd... hm. Resident Evil 4 I guess, the main story mode is good and the minigame where you kill all the zombies you can before the time's up is fun.