If your bike only has a basic LED panel, then the flashing lights could be indicating a fault in the system. Make sure the battery is charged and check it's connectors are clean and tight. Check the other connectors for water ingress as this can be a common problem. If you have a throttle fitted to the bike, disconnect it and see if the bike works with the PAS. Also disconnect the brake cut offs, if fitted. Post a photo of your control panel, this will help identify which system your bike has.
There is no throttle its magnet driven with sensors. The shop looked at the connectors and said looked like water was in the controller but there are no parts on eBay or anything to buy. The battery is perfectly OK and charged.
If the controller is water damaged, then it is most likely to be the problem. Is it in the base of the battery holder? If, so this should work as a replacement with a new display. Your motor should not have suffered any damage.
I think you will struggle to find a seller in the US with this type of controller, but by all means look for yourself if you prefer. Many here in the UK buy our parts direct from China and generally the deal goes OK. Where ever you buy, I would recommend you also get new pedal sensor, brake levers and throttle if required, from the same seller, as the connectors may differ with your existing ones. The whole kit from the link I mentioned in #5 is around £100 with postage.
The cable you have arrowed is the screen/handle bar display connection, it carries the power and comm's from the controller, so reason why you have no display info.
Show us a pic of your old controller and display cable connector.
You need the old connector/cable from your old controller and need to do either of two options.
1. Cut the end plug (old) off with plenty wire length and solder join the old connector/wires to correct colour wires on the new controller.
2. Unsolder both cables noting their position on the PCB (take pics) and swap them over soldering old cable to new controller PCB.
Before cutting any cables/wiring 100% make sure all items are from the same manufacturer, will probably be either Kuenteng (KT) or Luishi one isn't compatible with the other as some functions may or may not work. The name should be on rear of display and on controller label.
If not wanting to solder wires direct to PCB as replacement I would be inclined to solder and insulate wires still within the controller housing if possible for neatness and weather proofing.