I had an issue with my new T-61 recently where I would put the laptop in hibernate mode, only to have it start back up about 5 seconds after shutting down. At first I thought there was something defective with my docking station, but trying the laptop on a separate on yielded the same problem.

After a little more digging, it turns out that the problem was the result of BIOS and driver settings. You see, for some reason the Network setting in my BIOS had Wake on LAN set to Yes. This meant that when my laptop was connected by cable to a network (such is the case with my docking station), any network traffic coming to my machine would cause the laptop to wake up from hibernation. Simply turning Wake on LAN off, however, didn't solve my problem entirely. I also needed to go in to the properties for my network adapter (via Window's Device Manager) and turn off Wake on LAN there as well (for me, it was under the Power Management tab). Once I took care of this, my hibernation restart problem went away.