Turns out it wasn’t a bad logic board. All they did was replace the hard drive.
FedEx dropped it off to me at El Casa today, I turned it on and it booted right up. Applied all the updates and put the 2gb of RAM back in and everything appears to be good to go.
You do know, of course, that I will be performing regular back-ups on this device now, right? Good thing I’ve got that 250GB external drive sittin’ on my desk at home.