I'll come get that nasty ol' C3 and Leslie out of your way!

:twisted:
But seriously,
Don't throw it away! A new replacement is going to cost you $10,000 to $20,000! And it just won't be a tone-wheel Hammond!
The drawbars need to be cleaned and lubricated. B3Wanne is correct in that the Leslie problem is most likely the switch. From the condition of the drawbars, I'll guess that the tone generator needs to be lubricated and the tubes (organ preamp and Leslie) probably need replacement. Also, the buss bars will probably need cleaning (the switch contacts under the keys).
(And don't replace the tube preamp with a solid state model. Unless it caught fire and burned, I wouldn't replace it.)
You need a qualified organ tech. Try this link:
http://www.mitatechs.com/Also, check with a local music store, they may know of person who does this work. (But, if I could, I would use a MITA tech who works on Hammonds. It won't be cheap, but it will be a lot less than the cost of a new instrument.)