Well, that didn't last long. I brought the old laptop home on a Wednesday, installed Firefox and Chrome (they don't even bother trying to look like Mac programs any more, do they) and let it sit overnight. Worst problem was the battery drained quickly.
The next day I put some strain on it. I downloaded my MP3 library from the PC over wifi, while copying my old backup drive onto the desktop. Once the music was done copying I fired up Time Machine. Not too long before I went to bed, Time Machine finished its backup and the computer went to sleep. On the downside it never woke up.
Friday night I tried a couple things to no avail, then Saturday I took it to a friend's house to try booting from an install disc and running Disk Utility. No dice, it wouldn't boot from DVD either, so the thing was pretty thoroughly bricked.
Back to the repair place it goes and yeah, the motherboard crapped out this time. The fact that it's dead wasn't a surprise, the fact that it didn't appear dead the first time they tested it is. They're waiting to hear back on prices (which I'm kind of half-assuming means they're waiting for eBay auctions to end) at which point they'll give me a price on that repair plus a replacement battery.
To their credit they realize that "different part of computer dies two days later" is kind of out there and indicates something that could potentially have been caught earlier, so they're considering this batch of diagnostic work to be a continuation of the first time. So there's that anyway.