I put in a new battery, it worked for 20 minutes,

Usually, this is a case of overheating of the processor or other component. I would get a few cans of compressed air you get at an office supply store and clean all the compartments out as well as paying close attention to the fan grills and vents, blow all the hair, dust and debris out and clear the cooling fins. If it has been running for a long time with this clogged up grills it may have overheated and dried out the thermal grease on the processor and heatsink, if this is the case, the heatsink will need to be pulled and new thermal grease applied so that the components can "bleed" off heat.