I'm no expert, but for the sake of some shadetree troubleshooting; Do you have the manual?
Run through the basic and advanced settings, clear the memory, and make sure nothing has been messed up. I'd switch the power meter to voltage and check that it's giving you at least 48V (full should be over 50) and not hitting the low voltage cutout as soon as you give it power (battery could look good on the LCD meter when unloaded, but cells are toast and can't supply anything). That battery may be original to that year, and certainly would put it in the age range for possible failure.
Then start with the sensors next. Try all the functions to see if it is a general controller fault, or just under acceleration. Is the problem present in all assist levels? Does walk mode work? Do the other display inputs work? Lights/etc? Any error codes? Does it start up with cadence at all? Is the cadence sensor present and aligned? Unplug the throttle and try it with the cadence sensor only to rule out a physical throttle fault.
Then open up the controller housing (Bottom bracket) and unplug the controller and check it out. Make sure it's fully separated from the power and display completely and reconnect it to see if it resets any bad settings. Obviously looking for bad connections, wire cracks, etc. Wiggle and jiggle while you're in there and look for intermittent faults/resets.
After you have cycled it several times does the hub have any smells at all?
If you get the similar fault with all throttle requests (thumb/PAS/walk mode) then I would say the controller is possibly the culprit. If you only get the problem with the thumb throttle input, swap that first or test with it disconnected. If you don't find anything obvious, it's probably time to get deeper with a multi meter and test each component for draw and continuity...