IBM T40 Screen goes off after few seconds

survival,
Here's a couple of things to try:
Power down and remove the battery. Leave it out until you are done with the following procedures. Remove the memory modules and put only one back in. Try to power up. If that works, replace the other one and power up. If that works, you're fixed!
If not, try to power up in safe mode and see what happens. If it comes up, try running diagnostics on the HDD. If that fails, try reseating the hard drive.

Let me know how you're coming along on this. May be able to come up with more ideas, if needed.

If you need any additional information, please feel free to ask. If this information has assisted you in the resolution of you problem, please return here to give my assistance an appropriate final rating. If this information has answered your question and/or lead to a resolution, please rate it as "Fixya!".
Thank you, and have a super day!
Ron-

Well, being a techy I figured out this problem but not a fix. I have 3 T40 laptops with the same issue. One of them if you don't touch it it works fine. I probed around thinking the same are you , memory swaps and such but the problem seems to lie either on the motherboard or the CPU socket. When pressing my finger directly on the CPU it immidiatly freezes after making video glitches and garbage. It seems that the sockets become either faulty over time or the mother board has bad connections. I've tried swapping CPU's so that's not the issue. depending how much your CPU fan screws are tight will probably affect it's functionality. I just wish there was a real fix for it but it seems either mechanical or cold solder joints.

no luck when i tried your solution..