Trouble-shooting tips?

[brendala]

So, my desktop computer refuses to turn on (I'm currently using the old laptop that I gave to my mom a few months back). And, like a dumbass, I've been lazy about backing my stuff up on the external hard drive lately. So, if I can't at least retrieve the files from it, a TON of scanned drawings/photos/etc are going to be lost.

So, I just thought I'd ask anyone who might be tech savvy and/or has had this problem before what's up. Maybe I can at least troubleshoot this myself before I shell out cash for professional help.
I have a buddy who is a computer whiz; but it's hard to coordinate our schedules to get together and I don't want to wait too long before trying something. I also heard that a dude who handles the servers at my work might have a side business doing this sort of thing; so hopefully that pans out.

I just REALLY hope I don't have to resort to Best Buy's Geek Squad. In my experience, they tend to be inexperienced kids at best and and outright shysters at worst. >_<

Any advice would be appreciated!