I couldn't figure out how to get the 6 disk changer in my '04 Expedition head unit to work again. Cleaning it didn't help and I found no obvious broken wires, damaged contact points or moving parts. I was able to open up, clean and lubricate contact points for the 5 or 6(whatever it was) disk changer in a Chrysler minivan though and it worked for a few more years. So hit or miss, but if you like to take things apart give it a shot, they really aren't that complicated.
If yours is single disk CD player you can try blowing some compressed air into the slot liberally. It won't hurt.
I replaced mine with an aftermarket head unit, well I replaced the entire system, and have been much happier. I also took every CD in the house and copied the music to a USB flash drive that's plugged into the new head unit. Windows Media Player makes the copy process quick and easy.