Plug in, which has reset button, will click on and off sending intermittent power to pump. Resetting does not correct. Seems to be a relay; can you replace?

If I understand correctly, your power washer has a cord with a reset button on the plug. That would mean that the power cord is a GFI protected cord. It should only click off if it senses a ground fault. It should not click on until you press the reset button. If that is what is happening then you have a ground fault in the machine and the GFI is doing its job. You must find the fault and correct.
If it is clicking off and then clicking back on without you resetting, then the GFI is faulty. No repair, you can only replace the cord.

These are very sensitive to ground faults. You will need to check it with a meter until you find the fault. Use the highest setting on the ohms scale. See: https://dl.dropboxusercontent.com/u/8010163/How%20to%20use%20Test%20Equipment%20Service%20Manu al.pdf