Running a wire with a "momentary" switch under the dash creates a chance for crashing the car. Here is what happen. One hot day afternoon after shopping, you jump in the car to go home and try to start the car. You turn the key and the starter makes no noise. You remember the monentary switch under the dash. You turn the key to "on" and press the monentary switch. Car starts and moves forward crashing to car parked in front of you. Reason: The automatic tranny was still in D when you pressed the monentary switch.
Two of my cars have a wire going into the starter solenoid. The other end of the wire is connected to a lamp instead of a monentary switch. If the starter is not engaging, the lamp will tell me if the problem is in the starter or the electrical circuit.
In addition to the suggestions from Donnie, Larry, and Mike, check all the big ground cables to be sure good connections.