Are you sure you have a good ground connection between the battery and engine (starter)? An overheating clutch switch should not get hot enough to ruin a clutch cable.
As said, it sounds like it could be an issue with the TO bearing slide area on the tranny snout. So you'll have to drop the tranny, to check it out. It could be that the slide area needs to be cleaned up and relubed, or the TO bearing could be bad and be binding. It could also be a problem with the pressure plate on the clutch. Could also be the shaft in the tranny is broken. Whatever it is, once you drop the tranny, you should be able to figure it out.