Why is the fan spinning when it shouldn't?
The computer seems to be working quite hard at doing nothing. I can't get the fan to stop spinning.
The computer could be overheating. If there is too much dust in the fan area the fan won't be as effective and will spin faster than it should be. Additionally the thermal grease between the CPU and the heatsink could be too old and need to be replaced. Try first cleaning the fan area with compressed air and if that doesn't work try replacing the thermal grease.
The heat sink might be clogged with dust or there is a heating issue within the computer. I suggest disassembling part of the laptop and taking some compressed air to remove the excess dust. This should clear up most of the problem and allow the computer to run better.