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Another possiblity would be to trade it in on your replacement car. Some dealers will do 1k trade in value no mater the condition of the car. This is if you are buying from a dealer and the dealer isnt shady.
If they a dealer gives him a grand on his non running 1997 Blazer, they are going to add $1500 to the price of the car they are selling him. No dealer has ever "given more than the car is worth", ever. You are almost always better off selling a vehicle yourself, and in this case definitely. Put it on Craigslist, make sure that you clearly point out that the motor is bad, ask $700 for it. Find out roughly how much the vehicle weighs, then call a recycler and find out how much they are paying for scrap metal. You can try junkyards, but my experience is that they want your car for about half of what the recycler will pay, the shitty thing is that they are going to part it out, then sell it to the recycler for more than they paid you.
ETA: Definitely try Craigslist first though, chances are that there is somebody in your area with a wrecked Blazer looking for a nice body for his drivetrain, and will be happy to pay you more than the scrapper to get it.