I had a Lenovo T400 which didn’t boot, didn’t start at all. Wouldn’t even get to the BIOS screen.
During my research I found numerous articles with fixes.
In this particular situation it was the BIOS Battery which fixed it, apparently if the laptop is drained completely of power and left for a while the system refuses to start up again.
So you need to remove the screws from the back which hold the wrist rest and remove it. You will see the bios battery either next to the trackpad of under the keyboard.
Remove the battery for 30 seconds and put everything together again.