Check the SRS yellow connections to and from the clock spring. Also check if the horn works as that runs using another pair of wires within the clockspring spool. .. These things can be a problem if they are rotated whilst off the car as the internal wires are fragile and can break if stretched by too many turns. Best take off the car (with battery disconnected) and check the clockspring for continuity. Fortunately 2nd hand ones are usually available if it is shagged
The pump works on battery voltage so the bypass you have done just provided it with battery voltage which it is designed to run on. Did it make any positive difference starting the car with the bypass wire in place ?