No answers? Oh well -- I'll have to give it a try, just so someone can disagree with me:
This is most likely from dried up castor oil that's turned to varnish. The stuff can get pretty hard if it sits long enough. Fortunately it's a good metal preservative and fairly easy to remove.
If you don't have Cox wrenches, get a pair. There are some variations, so you want at least one wrench that'll fit your cylinder.
If you have wrenches, the first thing I'd do is to take off the head and visually inspect the cylinder and piston. If it's a big ball of rust, or if the cylinder walls are obviously galled (a bit of scuffing is normal, I'm talking about big gouges or rough spots) then you'll need to replace the piston and cylinder. If it's castor it may not be apparent, or there may be some dirty brownish-looking varnish in there -- that's a good thing. If there's really light rust you may be able to salvage the thing, although you could probably earn enough for three engines flipping burgers at MacDonald's in the time you'd spend restoring the engine.
If it's not rust, try heating up the cylinder with a heat gun -- you want it somewhere between "ouch" and "sizzle" -- and see if things will turn. If they do, it's castor and all you need to do is disassemble and clean.
Now, whether that worked or not, take the tank off (you need to do this anyway, because if the piston is stuck then the reed valve is most certainly in need of cleaning). At this point you would like to take the cylinder off. There's only two reasons not to: one, the piston is stuck all the way at the top of the cylinder, which means there's nothing to accommodate the upward motion of the cylinder as you unscrew it from the case, or two, the rod is stuck tight to the piston and will get twisted off as you turn the cylinder. So look at the piston's position in the cylinder, and if it's OK then take a pair of needle-nose pliers and try gently turning the rod. If it appears to turn, and if the piston's not too far up, then take the cylinder off the case. Now you've isolated your problem.
If you didn't unstick things with the heat gun and you still think it's castor oil, then the best thing to do is the antifreeze/crockpot thing (Google for it, or ask for clarification). Do the whole motor, as disassembled as you can get it. If that frees things up, then just clean everything thoroughly, replace your gaskets, and go fly.
If it doesn't respond to a hot bath in antifreeze, or if you just know it's rust, then try soaking just the cylinder and piston in penetrating oil. WD-40, CRC, kerosene and motor oil, or whatever your favorite is. Give it a few days to creep into the space between piston and cylinder, then see if things move. If it still doesn't free up, then you probably want to start thinking of measures that involve blocks of wood and hammers -- check back here before you start whacking the thing with a hammer, though!
In the end you should get the engine down to a pile of nice clean parts (I go as far as taking the crank out of the case, and scrub each part individually). Then get a rebuild kit, reassemble, and see if it all works.