"The way I fixed this problem, in all its manifestations, was to RESET the Plan Setting for the Power Plan back to all defaults! I had been playing around with some advanced settings, and noticed that some advanced settings parameters did not agree with the same parameter values for the basic settings, for items like sleep and hiberation.
I can only speculate that there are some subtleties of the Intel CPU sleep modes, that can be set from Windows and are persistent across a reset or even a complete shutdown. And I can also speculate that between Windows and the T61p BIOS, there are some bugs in the way that these settings are configured.
In any case, once I did the reset to defalt, I can put my system to sleep or hiberate or shut down from Windows, and the system always restarts when needed. I can also put my system to sleep by closing the screen lid, and then restart by opening the lid."
This part especially.