Problems with power-on button on T60

[FrederTM]

I own a IBM T60 2007-63G model and I had a complete swap of the mainboard and graphics memory. This works fine. Unfortunatly there´s a new problem:
When powering-up my thinkpad, the power switches on for half a second but then powers down again after half a second. Sometimes it powers more up, I can hear the fan working and the hard disk but the screen remains black. So I have to press the on button up to 50 times to finally get it working. This error is independent from the batteries or line power supply or if any other external devices are switched on. But I think that this problem is more common or visible in the morning or when the computer is physically cold. If the computer is powered down and up again it shows no problems.
Any ideas how to solve this problem?

NB: I have still carry-in warrant left but the next service shop is far and my bills and proof of purchase are 1000km away.

Hope you can help.