have you tried removing the battery while it is on the charger. It shouldn't need it to run. It sounds like you don't know enough that you should be attempting to fix that laptop from the way you've been talking. I'd save your money for one that won't need to be repaired.
If you did know what you were doing, like I said, I would pretty much disassemble the laptop to get all the dust out, chances are if your overheating that bad canned air is not going to help that much being that the dust is probably really packed into some tight places. Since you would already have it apart I would redo the thermal paste as well. This whole thing will be time consuming and not for the faint of heart so given your responses I don't recommend even bothering.
The beeping your getting is probably the laptop saying it is getting to hot or it is a post error. You are very unspecific which makes it very hard to give you much for ideas. As for the people saying to underclock it, good luck with figuring out how to do it, chances are you won't find a way.