Thank you guys. I think all info are useful. You can always learn new things. I became a very lazy user and forget many simple things in the past few years.
I tried to avoid anything related to Windows reinstall. For first, I realized that even Windows does not load up. Then I replaced the card again, and reduced the resolution to basic with the old card, and removed its old driver. And before the reboot, I put in the new card. By pressing it perfectly into the AGP slot, for 2nd or 3rd try, I reached to the state, that Windows started running, and I opened this thread

Then I tried DXDIAG, and realized Direct3D is bad...very bad. I red on forums, it must be a driver problem. So I tried several combinations of driver up and down installing

I checked the Device Manager too, if I have multiple drivers maybe, but that was okay. I even tried to disable the onboard sound chip, because that helped for some users

And somehow, the original "old" driver that came with the card started running fine, and now it is stable and fine. This new card is an Amper-eater, so the only thing to worry about now is my noname 400W power supply.
Thanx again for the tips. I will try to keep in mind them for future...who knows. My Windows install is some 3 years old now, but I felt this is NOT the right moment to reinstall it
