2000 Daewoo Nubira SE 2.0 liter 4 cyl. w/auto transmission & 124,000 miles. At times will not start when the ignition key is turned. There is no clicking from under the hood at all (no noise at all). If I go under the hood and bang around the transmission on the driver’s side near the firewall it will start normally. If while trying to start, I put my foot on the brake pedal, I will hear a clicking sound from around the gear shift but still no start.

The first thing that I would check is the Neutral Safety Switch.

Starter or starter solenoid.

Turn the key on. Step on the brake. Put the shifter in N instead of P. See if it starts.

If it does, or if it starts after you wiggle the shifter around, then either the neutral safety switch is bad or the linkage is out of adjustment.

starter solenoids usually click when they are failing because the conn. terminals are bad, but sometimes it they will fail without clicking sounds, because the actuating coil has gone bad. The test JWB describes is a good one, try it. If it does not do the trick, then have the starter removed and bench tested.