I finally got a new computer after 6 years, I am running Win 7 Premium Home on a i7 860 processor, 8GB RAM and a 1GB ATI Radeon HD 4850 video card.
After reading some of the posts here, I was scared of installing my Civ 4 discs, I know how my luck usually runs. Here is what I did:
* Installed the game from my original Civ 4 discs, ( had forgotten this game was on 2 discs). I opened Explorer and clicked Setup and clicked on Run as Admin and installed everything in the default directory. I then started a game (right-clicked on the desktop icon and Run as admin), went through about 10 turns, saved, exited the game. I started the game, again Run as admin from desktop icon. Everything seemed to work fine.
* I then installed Civ 4 patch 1.61, which I had copied from my old computer on a usb flash drive. I installed that also as Run as admin, and repeated all the steps above. Everything ran fine.
* I then installed Civ 4 patch 1.74, which I had copied from my old computer on a usb flash drive. I installed that also as Run as admin, and repeated all the steps above. I got that shader error message, but I followed the link provided by Ori in post #74, that fixed that problem (Thanks Ori!). Everything then ran fine.
* Next I found my old BTS discs, and followed the same procedure as installing the the original Civ 4 discs. All OK so far.
* I installed both BTS patches (4.17 then 3.19) as above, all seems to work OK.
* I don't really play Warlords that much, but since it was going well, I also dug out my original discs and installed them as above. When I went to play them, I got my first problem. I got a runtime error, so I tried to start the game again and this time it ran fine. I also installed the Warlords patch 2.13 and that went well too.
So, basically I installed everything as Run as Admin in the default directories, and so far so good. Now I am going to try a few mods (Rise of Mankind and maybe Total Realism) and see if I can get success from them too!
Thanks everyone that that has posted in this thread!