From experience with this model it has a common issue with the Intel chipset going flakey. Usually the USB goes first followed by the symptoms you describe. The cases are small and the cooling isnt great so failure is inevitable at some point.
Given the age of the machine surely the most sensible course of action is to replace it with a new unit? I can understand that they may not wish to pay to replace all the PC's but surely the £50 you would spend on a new board is better going towards the cost of a new system? You can build a basic Pentium dual core PC with off-the-shelf components for less than £200 or alternatively you can pick up a refurbished Dell Optiplex 3020 for £210 + Vat on the Dell outlet.