I also have a dead Apollo 1240. In my case the fan came detached and the cpu has overheated and fried itself.
There is a guy on here, PG, who will probably be able to fix it for you. I keep meaning to get in touch with him about mine, but never have the time as I am working away from home right now.
He has offered to try and upgrade the cpu to a 68060 and see if this fixes the problem. If it doesn't the only cost will be return postage.
I don't think he hangs around here much so probably better to email him rather than private message him.
Good luck!
