If all of the above parts test good then please let us know and we will take it from there.
Those look like the original batteries so I would not have too much faith in them maintaining their Voltage under load. Only a load test will determine if they are good or bad though.
Maybe the photo is hiding a wire because the throttle only looks like it has two wires to me. The SPD-24250B controller requires a three wire throttle. Hopefully the throttle has a green wire that I am not seeing though.
Please let us know if you have any questions.