Hi again,
I finally got some free time and did do a lot today starting from the morning. I had cleaned the CPU earlier this week and after cleaning the it, the CPU didn't look that bad as I initially thought. Earlier this week I had bought some thermal grease and applied it. This was the first time ever I had installed a heat sink myself and I'm happy that it went well.
The biggest problem after installing the heat sink was not the CPU. It did work and computer booted, but I just couldn't get any signal from the S3 Trio video card. So the screen was black all time. I did try with some other old video cards too, but they didn't either work. So I spent extra hours when having to remove the motherboard a couple of times. I suspected a short circuit, but after examining the bottom of the motherboard, couldn't find any evidence of it.
Finally got it anyhow working, but don't still know what was reason for the black screen on computer startup. (The motherboard is AK75-EC and had never heard of it before I got this PC.)
According to the BIOS, the CPU temperature was also okay, so the CPU was not damaged. After this I also installed Windows 98, replaced some IDE cables, new hard drive etc, DVD drive, so there was quite much to do. Finally installed my old Sound Blaster Live (CT4670) card that works well, but doesn't sound as good as I expected in DOS mode when tested some games.