[CORed]

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If only there were a government agency or department that dealt with motor vehicles. They would really be the perfect people to talk to about this.

But since there isn't, just take it to a chop-shop. No one will buy it without a registration.

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I've sold a car without registration, but it was a complete junker that I sold for parts for $300.

Whether OP can sell a car without registration and inspection is going to depend on the laws of the state he lives in. In any case, the market value will take a big hit if he can't get it legal. Unless repairing it to pass inspection is going to cost a lot of money, he's better off getting it registered and inspected.