Here's an interesting clip during a broadcast of the 1985 PPG Indycar Series:

1985 CART Indy Car Team Cost Featurette

The price they come up with for a competitive single car team is $2.3 million, which includes purchasing new chassis, engines, transporters and equipment, hiring a team and a "test team" budget. See the video for the breakdown of costs.

I ran that figure through an online "inflation calculator" and it comes to about $4.54 million in 2008 dollars.

Interestingly, that's not too far off this 2006 estimate of $5.47 million to run one car in the current IRL Indy Car series. Of course, that's after numerous cost cutting attempts by the IRL. As of 2009, the series still uses the same cars and engines as 2006 and there has been more cost cutting but who knows how effective.

During CART's peak in the mid to late 90's, budgets were rumored to be $10 million + for a car.