Finally fixed the problem. Going into the Steam menu I right clicked on Far Cry 2, selected "Properties" and clicked, "Verify Integrity of Cache..." After selecting that, Steam found a problem and fixed it. So any Steam or other folk downloading from other pay sites, that may be worth a try. Unfortunately, Steam didn't explain exactly what was wrong with the cache nor what it did to fix it, but that might point those wiser than myself regarding computers in the right direction.
Again, thanks for all the help guys (and perhaps gals as well). Now I'm going to go run around like a lunatic with my flame thrower and machine gun.