Retail book (www.nada.com) $6000 to 19,000
Not enough info from you on your car.
Coupe, conv, engine, ??????????????
Deduct for needed repairs and cosmetics

eBay bad idea,try craigslist.com or the newspaper,trust me better results,eBay you see dead bets!

35,000 miles??? are you sure it’s not 235,000 miles?

i have a 79 vette with 190,000 miles. it’s worth between 5 and 8 thousand bucks.

i think about 200 grand

I searched a few “completed” listings. Two Vettes NOT sell, their starting bids were $3,500 and $4,000. But, they just regular nothing special like any other used car. There was one that was “Cherry” very nice and well restored/maintained, it SOLD for $10,500.
Ebay can be hard selling a vehicle, people have to drive to see it, and, it not close, they not drive, unless it is something VERY Special. What you can do is decide what the Minimum you would take and start the Bidding there, for those I seen, maybe $4,000-5,000 for a start. I have a friend he tried to Sell a Car & Harley on Ebay, which you do have to pay some money to list, he not sell them. They finally sold locally advertising them in the Classifieds of the local newspaper. Good Luck.
From your added comments; If you do list it mention the New Engine and milage, HAVE Reciepts if someone want to see etc. Every little thing you think of to help gain interest helps. And have some good Pictures so people can see the Car. Interior/Exterior.