Make sure to test the RAM slots. These old MacBook boards constantly develop bad slots over time, and if a bad slot is occupied, a machine will behave similarly to what you describe. Take one module out and test the machine, then if that does not fix it, fill the empty slot and take the other out.
Resetting the PMU/SMC is good, and also, if testing the RAM slots doesn't help, take off the topcase and disconnect everything that is unnecessary -- optical, hard drive, battery, sound, Airport, etc. If everything is disconnected and it still behaves the same, you know it's the board.