My T61p did the same thing last week. Running fine as usual, turned to talk to someone and when I turned back, everything was dead. Not even the AC power indicator LED was on. Tried power switch, unplugging from docking station, switching batteries, letting it sit for 15 minutes connected to no AC or battery--still dead.
Sent it in to Lenovo for warranty repair. They said there was corrosion on the motherboard, so the repair was not under warranty and wanted $750 to fix. I had them ship the T61p back to me (I didn't think of asking for them to take pictures and send the pictures instead

).
The "corrosion" is a very small area on the bottom of the motherboard by the radios switch on the front of the T61p. It seems clear to me that the problem has to do with the power circuitry, as nothing else I can think of would explain the AC power LED not going on when I plug the T61p into the AC adapter. Further, it would seem to be a sizable failure to cause the laptop to go from working fine to completely dead in a matter of seconds. Now I know that a short anywhere on the board could theoretically cause a failure in the power circuitry, but I would not expect "corrosion" around very thin traces on the opposite end of the motherboard from the power circuitry, without any signs of heat damage, to cause such a sudden and complete failure of the power circuitry.
What do think?
Photo and links to more photos below.
http://home.earthlink.net/~wmonroe/site ... up_top.jpg
http://home.earthlink.net/~wmonroe/site ... bottom.jpg
http://home.earthlink.net/~wmonroe/site ... de_top.jpg