In most areas there are "dealers" who specialize in used appliances. Some of these people are unlikely to be members of the "Better Business Bureau" so you have to ask around a bit to find out if they're reliable (or even competent, in some cases).
If you can find one that has a fairly good reputation you might be able to get him to take the old one so you don't have to mess with it. You're not likely to get much if any "trade in value" for it, but bulky stuff like dryers are something of a nuisance to try to find someone who wants to provide a home for one - especially one needing repairs.
Most more "establishment" dealers may have used/repo/trade-in appliances; but some don't bother with them unless they're "exceptionally clean," and for one of these their prices won't be rock bottom. Any established dealer should be willing to dispose of your old one for you, and unless you already know someone who really wants your old one, I'd suggest working the removal of the old one into the deal to get the replacement.
Local conditions can affect what's best; but if it doesn't work, and you don't want to fix it, you're probably best off to look for the simplest way of getting it off your homestead.