Car themed games are popular.  I don't think you would get anything for under $1k or even close (DMD).

Nino (Strangeways) might be able to help you with an EM car racing game, but they would still be pricey.  I have seen a corvette that Nino has and its sweet.

Off the top of my head Getaway, NASCAR/Grand Prix/Dale JR are pretty popular.  (around the $2k to $3k mark).  Then older titles like Memory Lane etc.

Otherwise Viper Night Drivin' can be picked up pretty cheap but I would strongly suggest playing one first before even considering.  Most prefer Getaway & NASCAR series etc.