I've serviced and rebuilt many a judy, from xc, sl and the lovely fax.
If your forks are fully compressed, it means the blastomere inside are shot. If they were spring internals it wouldn't happen. If you are lucky, they have crumbled to dust, if not, they may be a gory sticky puddle within.
To find out, undo the top caps on top of each leg, if the crown has two bolts either side, loosen these first as they can crimp the stanchions against the caps and make it harder to unscrew them.
With the caps off (or do one at a time), tip the fork upside down and shake the contents out. This could be messy, so do it somewhere easy to clean up afterwards.
I forgot to mention there are 2 types of cap/elastomer arrangements. One has a skewer attached to the cap that the elastomer slide on, with a plastic disc spacer in between each elastomer, the other doesn't, instead the plastic spacers have a nub sticking out each side which pushes into the elastomer hole. You'll know which you have when you unscrew and remove.
Either way, you'll have elastomer mess inside that you'll need to clean out.
The best way to do this is to remove the stanchions from the lowers, and remove the damper and dummy leg from each side respectively.
This is easy to do, but can be daunting, especially if you find you have a plastic damper body, as this is often brittle after all those years hiding in the stanchions, and removing it can be the end of it if unlucky.
That aside, to do it, undo the Allen key bolts on the lower legs. One might have an adjuster that needs removing first. It should just pull off.
Before the Allen bolts are completely unthreaded, screw them back on so a few threads are inserted, then hit with a rubber mallet to break the taper. I find it best to hit the Allen key rather than the bolt with the mallet. Once the bolts have moved, the taper is free. Remove bolts and pull stanchions from lowers. Feel free at this point to inspect the bushings and give the internal legs a clean and dry.
To remove the damper and dummy leg, there are circlips on the bottom of each stanchion that need removing. Once off you should be able the pull them free, or you can push them out from the top using something long and thin enough to fit inside the stanchions. I have an old wooden broom handle that fits a treat.
With the stanchions now clear of anything, you can clean them out. Soapy water first to get out the remnants of anything, then I'd use isopropyl alcohol after to finish the job. Go easy, you don't want to scratch or damage anything. The broom handle comes in hand again as it's soft wood compared to the stanchions and you can push a soft cloth through to remove any crap.
Hopefully the outside of the stanchions are clean and free from scoring and putting, if not you may want to reconsider cleaning the insides and find some new ones.
If all's good, next thing is to check the damper. If it's not leaking, no scoring to the shaft and had a good resistance when you push and pull the rod through the body without any gaps that could indicate oil loss, I'd clean it and reuse as is. Also at this point you'll know if it's plastic or metal bodied. If there's anything wrong with it, especially if it's plastic, you are probably better off replacing it with one of the same length shaft.
Clean and check the dummy leg. This is a mess critical part in terms of condition, but it's still nice to have one without and scoring or issues.
If everything is good, refit as they came out. I'd lube the shafts with some suspension grease first to ensure a slick movement.
At this point you can refit the stanchions to the lowers. When you tighten up the lower leg Allen bolts, don't go crazy with torque or you can crack the lowers. Refit the damper adjuster if you removed on.
Oops, nearly forgot. Before doing this, check the condition of the wiper seals. If they aren't soft and are cracked. Get some new ones. If they are ok, you can pop them out with some leverage and a spanner, clean, refit and fill the void between them with Judy butter or other suspension grease. I also use a socket on an extension to smear the bushes in the lower legs with the same grease. There are some deep down, and the ones visible at the top of the legs below the wiper seals. If the bushings are worn, then that's a new ball game as replacing them requires tools and a spare set to replace them with
All your fork needs now is either some replacement customers or springs. Fit these, refit top caps, tighten the crown Allen bolts and that's that.