Hello, 

According to last years statistics, the minimum marks required to get a seat in government medical colleges under 85% state Quota in Tamil Nadu under BC category were 500. So I suppose you have a little chance to get government seat but results vary according to the cutoff. Good luck, I hope this helps !! 

Also, you can more colleges through college predictor in the link below, 

https://medicine.careers360.com/neet-college-predictor