It's a shame that the shop can't do basic diagnostics. It's not exactly difficult.
If they say the motor is OK, which is easy to test by connecting a 12v battery directly to the two motor wires, and the battery is OK, then either the controller, the wiring, the throttle or the PAS is faulty. Each, apart from the controller, is easy to diagnose, but not remotely over the internet because we don't know what you've got.
Controllers don't cost much. You can find them on Ebay for £15 to £20 without PAS. You need to be able to do basic wiring if you want to try one. If it were my bike, I'd give it a try, but I don't know your capability.