Ok i am not dreaming but my T500 turns on by itself even when it is shut closed -some times it does not turn on if you press the power
switch but then some time later turns on by itself,At first i thought someone is hacking into my system but then it did it in different
times and when it turns on i hear the windows welcome chime.Any one have a clue?

this seems to be a common problem, I have had this happen. and received no help from lenovo. do you feel like it overheats when you are doing anything relatively graphics-intensive?

I fixed it by either: buying a new battery, upgrading to windows 7 from xp, removing the intel turbo memory, or unplugging/replugging the cmos battery

Could you go into your device manager and see if there are any yellow triangles there? I'm just wondering if perhaps some type of driver that controls your hardware might be missing. Perhaps you may need to update one that handles power management. How are you settings in BIOS? Did you disable the options that enable a remote administrator to have priority over your laptop?

You should make sure "wake on LAN" is off, see if that helps. I had this with a T43, that solved it.