We recently bought a new winch as we had to cut our spare of our 2001 f250. The new winch assembly went down, but when we go to put it back up it just makes a ratcheting sound. Any ideas?

Most under body spare winches are driven by either a cross or a loop on the end of the bar. The winch will be a hollow bar with a slot cut across it so either will do the job. Remember that the winch is locked and requires some initial effort to release the clutch in the winch so that you can wind it down

that's going to be a dealer item unless you call around to the junk yards and hope fully they
might have one laying around

hope this helps you
bob

Replace the whole winch assembly, either new or used

I suspect a problem with the winch itself not realeasing the tire down.. If this is so, I believe the spare tire needs to be cut from the cable in order to replace the winch.

What's happening is that the latch is not releasing - a safety feature so the tire doesn't drop down onto the road should the cable or assembly rust/break etc. While researching I got this info from another forum: Jack up the rear of the van. Wind the spare "up". now put your jack under the spare to support its weight. Then "unwind" it. now look up through the spare to the winch assembly. You'll see a latch at the back - towards the rear of the van. Reach in with a long screwdriver and release it by moving it towards the rear of the van. If you've unwound the winch you should be able to move the plastic holder downwards. Once you've done this you can allow the tire to come down and remove it. Now remove the winch assembly - 5 or 6 bolts. Odds are you'll see apiece of wire hanging or it may have fallen out. You'll also see a spring clip - it clips onto the underside so when you unwind the winch it should pull the aforementioned latch to release the tire. You should be able to get this back in place by fiddling with it, or just attach a wire to the latch to work it manually. Or buy a new winch assembly - approx. $150. Good luck

I have a '02 TrailBlazer and I had the same problem. When I got a flat and went to change the tire on the side of the road I was not able to get the tire off the winch. Luckly, I have AAA and the driver knew the trick to getting the tire free. The process involved lowering the tire as far as it would go and then kicking it. Wind back up and repeat until the winch free's itself.

When I took the car into the shop to get the tire fixed and the have the spare put back on the car, they were not able to get the winch free enough to put the tire back on. They said that is is a common problem with this mechanism and suggested replacing the winch system (estmated parts and labor $215). From what I can tell the winch accumulates rust up in the cable and locks up.

This unfortunately is a common problem, you will have to cut the cable and replace the tire winch, luckily they are cheap.

The unit is sealed, a new one is cheap, this is an all to common issue on all fords, have answered 3 questions about the same issue today alone.

I had the same problem and the shop I took it to couldn't get it off either. But I opted for them not to cut it off and I took the truck home to diagnose what the problem was. So to make this short, I got the spare down and the only way you can do the same is by using a flat head screw driver, pliers, and some "Deep Creep" penetrating oil. 
First: if you have the tire down the standard 2" or so, take your pliers and pull at the base of the cable "downwards". (the cable should free from the bracket under the tire that holds it up).
-Then spray penetrating oil around the bracket as this is what is causing it not to release. In the manual it suggests pushing it back up with the jack until it clicks to allow it to come down. Most likely this will not work as dirt and corrosion will freeze the mechanism that acts as the secondary lock. 
-Take your jack and lift up your spare, holding the weight on the rim and not the bracket attached to the winch. This should free up the winch to allow movement. Then taking your flat head screw driver and you will likely need a flash light, look up into the hole where the cable comes from. You will see there are two little teeth attached to it inside holding it to the frame of the winch. First try prying the teeth away from the lip of the hole to allow the bracket to drop. If this doesn't work, then stick your flat head in between the sides of the arm attached to the teeth and pry outwards, allowing the arm to free up enough to allow movement.
This should drop your tire down and avoid the expense of buying another winch after cutting yours. 
Good luck!

Have someone pry down on the tire while turning...