I downloaded the service manual and took it apart, and I was horrified to see that the power connector on the motherboard was entirely broken off now, and that it apparently was being held in place with a small piece of electrical tape! Yeah, it was shipped to me from Taiwan with a piece of electrical tape securing a broken power connector on the motherboard.
Even more scary is all of the scoring from what I assume was a frequent short. I think I'm lucky the thing never caught fire.
I'm seriously pissed off about this, especially seeing as how I need the thing for my job. There's no point in me trying to put the thing back together, and I can't solder the connector back on. I can try to find a replacement, but I doubt I can find one that will fit the motherboard exactly.
Needless to say, I sent a very strongly worded message to HP about this. In the mean time, I have to figure out what the hell I'm going to do, because I can't stop working over this.