Time Warp sound board worked in your Flash. Flip that around, try the Flash sound board in the Time Warp and see how it goes. You want to narrow down the problem.
Did you check the chips and logic gates which drive the transistors? A $15 logic probe helps here.
Also as a general rule, some header pin solder joints are bad on most Williams games of this vintage, and the CPU <> Driver interconnect usually needs replacement.