please do this at your own risk...

i will try to get some picures out but all you need to do is take all the screws out of the bottom of the laptop this will include the screws that hold the touchpad on (they have covers glued on them) once you do this the keybord concole and touchpad concole come off just disconnect the ribbon cables. once this is accomplished pry up the motherboard in the bottom left hand corner just so you can put somthing under it (i used a littile peice of rubber i had laying on my desk. this will put reverse pressure on the motherbord that was caused by warping. i had to break off the door to my card bus so that i could still acess it. after it is proped up turn it on and see what happens you may need to try diffrent things to get enough levitation. then put the thing back together. like i said this will warp the shape of the handrest and make it look funny. ive had it working for 3 days now and have only had the problem a coupple of times... it works much better if left on a flat surface. But it works and is defintaly worth the troubble. i will be checking the tread every now and then so please dont be afraid to ask questions and i will help as much as possible.

I had a same problem with my T40 few years ago. Mine was a internal motherboard defect. your might be the same.
Actually, try removing your ram sticks and replacing it with different ones. It might solve the problem