Engine locked up after repair?

It would depend on why it locked up. If it had been leaking oil for a while the engine may have been damaged, and it didn't show until the leak was repaired. Without knowing how it failed it's hard to give an answer. If he's saying $4,000 for the complete replacement labor included, that would already be a large discount. A good used engine alone is $3,500 - $4,000 for a lower mileage used one.

It's a bad thing to have happened but unfortunately unless you tear the engine down and can show that the shop did something wrong when changing the valve cover, there just isn't a way to say, "Yes they were at fault." I suppose you could tell the shop it's at that you are going to send it to another shop (or better a dealer) to have that done. I might do that anyway if I doubt the shop that did the work like you do. Then it would be a situation where you get a lawyer and sue that shop to get all of their work and the replacement of your engine paid for, based off what the dealer shop finds. The catch there is that unless they found a true "smoking gun" like a tool dropped inside the engine or similar hard fail item you could lose.

You're welcome.