I would charge the system with 15# of water and if it has any leaks (be sure it is isolated from the house, if it isn't, I would doubt if you have any as they would show already), fix them. Get a wire tube brush at the plumbing supply store the size of the tubes, attatch it to a long handle and run it through the tubes to clean them. Clean everything up and make sure its lubed and free to function properly. Seal and close the exhaust end and you should be ready to go.
What kind of coal is in it? If its anthracite, you are one very lucky individual. Not too many people find a gold mine in their basement. If its Bit, your still pretty well off. Whatever it is, you have a ton to dial it in. How about some pics of the coal?
That thing was not backup, no one would install that thing as backup. It is the original primary heat source.
Ditto sealing the asbestos, do not under any circumstances allow anyone to talk you into removing it. The abatment will cost about $10,000 and your basement will become the warmest place in town besides the pizza house's oven (the house may get cold too, depending on how much punch that thing has, either way the cost to operate will go way up). There is nothing on the planet better for that job than asbestos. If any is loose, wet it before you play with it and wrap it with stuff from the supply house, its cheap. Then seal it up with the paint.Wear a very tight particale mask too.