Isn't the right thing for the dashboard to spit out the cassette player and for the owner to cough up the dough for something newer?
Take it apart, as eljefino says, parts get old and brittle, maybe you'll get lucky and it's a trivial fix. If not, well, I'm sure there's nothing on the radio worth listening to. Forget if there are cheapo cassette radios at Walmart or other places--as stated, even the newest one in the junkyard is getting long in tooth. Might be a pain to deal with a convertor but I never found it that big of a deal, at least not on the older vehicles that I swapped radios in.