W500 sometimes won't power on or power off after shutdown

[as]

I have recently acquired my first Thinkpad, a W500 (4063-3FU, apparently off-lease). It came with an additional 1GB of RAM, so 3GB in total, and I've replaced the 60GB HDD it came with with my own 120GB 5400rpm spinner. It sometimes doesn't turn on when I press the power button. Either nothing happens, or the battery and charger LEDs briefly come on (yellow and green resp.). It seems to be less of a problem if the charger is disconnected. After pressing a number of times, long and short (like the static discharge procedure), and connecting/disconnecting the charger, it usually turns on. Sometimes there's no problem whatsoever, but the problem seems to occur a lot more frequently than with others. The USB ports all look intact, I don't think any contacts there are touching. The charger is missing a small chip out of the connector, like it was scraped across concrete for a while.

It operates without hiccups in my experience, but sometimes after the OS shuts down, it doesn't power off - LEDs stay turned on, fans keep spinning.

I've done a BIOS reset by removing the CMOS battery as per http://www.tomshardware.com/forum/26943 ... oot-screen (and changed some settings afterwards). It seemed a bit better, but the problems quickly returned. I've tried repeatedly turning it on and off again (before the OS boots), which usually works, but occasionally it hangs on the BIOS screen.

I'm guessing the keyboard with the power button are not the problem, since I'm able to type up this post just fine and the button works most of the time. Maybe the CMOS battery is dying, but I haven't seen any date/time reset messages from the BIOS except when I left the main battery out overnight. I saw http://www.tomsguide.com/answers/id-222 ... -turn.html mentioning poly-fuses, which I assume could mean a motherboard replacement - something I'm not too keen on doing, since it would cost almost as much as the entire laptop.

[as]

The company which sold it to me took it back to fix it, and it worked as expected in casual use for a week or two. I then started noticing that it would not always resume from suspend (the moon LED would stay on when opened). Taking out the battery took me back to the original problem of it not turning on at all, or only occasionally flashing the battery and AC LEDs.

However, I recently had some success by grounding the touchpad (using a tap and my body as the conductor), which seems fairly successful at getting it to turn on again. It does not always work, and the problem quickly returns. I guess that at this point, a combination of the static discharge procedure (pressing the power button 10x for 1 second and 1x for 30 seconds) and grounding it are my best bet to get it working (briefly). This leads me to think that the problem is that the motherboard reacts to static electricity that is somehow accumulated - is this a known problem? Could anyone suggest solutions?

I have already disabled the ATI video card in the BIOS. Could it be that the motherboard somehow generates static electricity? Or is my charger possibly the source of the problem since the connector has some minor damage? Removing the battery when it isn't completely off certainly seems to make things worse. I heard batteries could retain static electricity as well, is there any way to prevent/solve that?

(In another thread I asked about replacing the motherboard, but now I'm wondering whether that is a solution - another component could possibly generate static electricity - other than the user.)