Temp gauge climbs to the max as I try starting the car. Car won't run.

Does the fuel gauge work? They are fed by the same IVR --instrument voltage limiter/ regulator. Try pulling the temp sensor wire off at the engine that should cause gauge to stay "cold."
What kind of ignition system is this? Mopar breakerless, GM HEI module, etc etc
Have you checked spark?

"What do you mean" "replaced distributor?" What was there before, and had it been working, etc

Have you made any wiring changes or repairs?

Bear in mind that "new' (rebuilt) does not mean "functional"