Tom's right, some parts could be sold. But the limitations were not well thought out.
First of all, since the program was only for new-ish cars, cars which many other owners need replacement parts for, keeping the big ticket items out of the recycling chain was a major faux pas in this age of Green enlightenment. And it was stupid and arbitrary.
I remember seeing some scientist using roadside sniffers and cameras to get an idea of which cars pollute more. In general it was older, non-high performance clunkers that were too old for the Cash for Clunkers program. The results of this study led some pollution control districts to run their own incentive programs, offering a few hundred dollars for people who drive a gross polluter (each bad one put out thousands of times more pollution than a single new car) to sell their car. In those programs, the cars were parted-out for recycling; only the bodies were crushed.
Cash for Clunkers was a needed economic incentive, there's no doubt about that. But its execution could have been better. Especially so since the people who drafted it had lots of previous experience to draw upon. From an environmental point of view, it would have been better to give the owners of cars with early and/or failed pollution controls a chance to get in on the deal. Sure, it might have caused a stampede of people getting the worst cars off the road. In my book that's a Good Thing. If they had the cash or good credit to buy a new car, then why not?