X220 - Reboots itself

[hhkb]

So I've been having this problem lately where my x220 spontaneously reboots itself about once a week. It's happened about 6 or 7 times when idle (I've left it alone for a while, not doing anything). It happened one time while I was actively using it. And just recently, it happened while the machine was suspended. In all cases except for the previous one, I had both the battery and either a 65W or 90W AC charger plugged in.

I want to avoid an on-site service call, because those guys are just plain clueless. I want to do ESC, but I'm not sure what the faulty part is. I think most likely motherboard, and then potentially the battery (although with AC plugged in, I'd assume the battery couldn't cause a problem). Any tips on further diagnosing the issue?