MacBook Pro :: Won't Turn On - Get Stuff Off?

My 2007 MBP won't boot up, or at least the screen won't turn on. The genius diagnosed it as an issue with the logic board. I'm not quite two months out of warranty, so it's $310 to fix -- but I spilled water on it three years ago, and if damage is detected, my repair options start to get pretty pricey. I'm now the proud owner of the base-model 13" MBP, which is great, though it hasn't been 24 hours yet. I'm still planning to send the old MBP out to attempt the $310 repair, and we'll keep it as a backup if they'll fix it. However, I'd really like to get my data off the hard drive before I ship it out. I keep hoping it will magically boot up -- it's come back to life a couple of times since I started having this problem -- but I can't expect it to.

What is the easiest way to get my info off the hard drive so I can load everything onto my new MBP? I don't want to do anything more that would give Apple reason to say they can't do the repair. I know I should've backed up, but I didn't, and I can assure you I've learned my lesson ... the hard way.