Acer :: TravelMate 2420 Overheating

I bought a used Acer TravelMate 2420 laptop (WinXP, RAM 1 GM, hard disk 40 GB, Intel Celeron M processor 1,50 GHZ) and since the beginning it had overheating problems and also some issues with power management. And yes, I know it was a stupid thing to buy it, but knowing it doesn't help.

Now the problems:
1. Whatever I do, it keeps overheating, even if no programs are opened. The laptop's fan works very vaguely, and I can hardly hear any sound of it. At first it didn't trouble me much, as it was winter and it would still work, although heated up. I also bought an USB ventilation pad (2 fans), and it helped for some time. But now, when the air temperature is over 30 degrees (in the room), the laptop just "freezes" in the middle of work and stays like this for about 20 min, or just suddenly shuts down completely.

2. I can't turn it off if the power supply is on - I have to unplug it just before the computer shuts down, otherwise it keeps on restarting. Also I can't use it without a battery, as it doesn't turn off in any way (even pressing the power button for a long time doesn't help), and I have to unplug power supply (which ain't no good for computer).

What I already tried to do:
1. Re-installed Windows, installed updates.

2. Checked the computer with various antivirus and antimalware programs (Avira, AVG-free, Malwarebytes' Anti-malware, Spybot Search and Destroy, Ad-Aware).

3. Installed additional Acer utilities: Acer emPowering Framework, Acer ePerformance Management, Acer ePower Management - but they basically didn't let me change anything important (like the fan speed, for example). With PowerManager I changed the CPU speed to Medium, well, it helped a little bit, but the comp. is totally slow now (and still overheats) ... if I set the speed to High, it just turns off after about 10 minutes.

4. Instaled SpeedFan to speed up the fan - but it didn't detect any fan in the computer!

5. Dismantled the laptop (removed the hard disk, the keyboard) to see if the fan isn't clogged, but I still couldn't reach it. So I just used a vacuum-cleaner as much as I could reach, but of course it didn't change anything.

6. Oh and of course I disabled all the unnecessary programmes (by modifying msconfig -> startup).

7. Ran HDD diagnostics, S.M.A.R.T. report showed no problems.

I've read quite a lot now about these laptops, and seems like they all have this overheating problem, but it's usually solved by using a ventilating pad (which helped in my case a bit, but basically didn't solve the problem). I didn't found anybody having these power problems, so I guess maybe a previous user made some stupid modifications... I just don't know how to fix them now.