I believe ESPNs first Cup race was in 1980 or 81 in Martinsville, IIRC. Races were covered sporatically throughout the 80s and 90s on a bunch of networks...ESPN, CBS, TNN, TBS (their coverage was typically horrible), and occasionally ABC. ABC popped up primarily with the first Brickyard 400. TBS always had the Atlanta races (surprise) and a few others. I've heard PBS even covered a race once...showed video coverage along with audio from MRN. Nearly all races were covered live by early 1990's. The last hold-out was the spring race in North Wilkesboro, because in always conflicted with the NFL draft, which ESPN chose to show live, and tape-delay the race. Finally this was resolved in 1994 or 95 and all races have been shown live since (save for one Brickyard race (1995 or 96, I believe?) that was rain-delayed and ABC chose not to show the race at all.)
NBC's first event was 1999 Homestead race. It was also terrible! FOX & NBC/TNT current contract took effect in 2001 and expires at end of 2006 season. In 2007, FOX keeps first part of season and takes over Daytona 500 every year. TNT will have a mid-season pack of 6 races or so, and the "chase" events will be on ESPN/ABC. NBC is out (thank goodness).