A friend gave me her dead 1st gen iPod Touch (her cat peed on it...). It is definitely dead. I am curious if there is any possibility of using the screen (or other parts) or if that would be a waste of time to attempt.
No idea.
Take it to bits, see what's in there and what you can figure out.
Her cat pee'd on it? Weird. Lol. 
Yeah. As I understand it, it had something to do with Justin Bieber. Guess her cat just couldn't take it any longer .. 
I would go online, find a disassembly tutorial, and then carefully (very carefully - you don't want to break it further, tear ribbon cables, etc) disassemble it, noting (and perhaps photographing) the process. Once apart, carefully look at everything under a magnafying glass (if you have a low-power inspection scope, even better!); don't neglect a square inch.
Once you have it completely documented, clean the boards and such; you might have to do more research here, but generally you want to obtain some specialty solvents for electronic PCB cleaning, plus some distilled water; after using the solvents (shallow glass pan, immerse the boards, agitate them, follow directions), blow them off with canned air, then rinse with distilled water, blow off again, then let dry.
Certain parts might be difficult to clean; depending on how the screen is constructed, its likely to be the most difficult. Likely, though, the issue is with a short caused by the cat urine and dissolved minerals causing shorts. Nasty, but fixable. You might have to do the cleaning procedure multiple times.
There's a good chance you might get a working i-pod touch out of this deal; beyond that, I don't know if there is much or anything you can do with the parts, given the likely extremely small pitch of the components and interconnects used by the screen and such (and, even if you managed to get it "broken out" for interfacing, the resolution and such precludes it from being used by the Arduino - I doubt the screen is a serial or low-parallel pin count device; it likely depends on a separate processor and memory in the ipod to work).
Good luck...
- battery
- wifi bits (maybe?)
- stereo jack socket
- front switch
- accelerometer
?battery - Maybe
?wifi bits (maybe?) - No
?stereo jack socket - Maybe but not great
?front switch - Not too great
?accelerometer - No way you're gonna get at that.