It just died while driving

[427TJ]

Driving my Camaro on the freeway at 70 and the engine quits. I look down at the tach and see the needle bounce a couple of times from zero to about 3000 but the engine is stopped. I coast to the roadside, put it in Park, turn the key and it starts. Runs a little rough for a second, I rev it a few times to clear it, it clears up and idles fine so I pull back onto the road to head home. A mile later it died again and I coast to the roadside again. I put it in Park, hit the key, the starter cranks for a half-second and then nothing. Nada. Zip. Move the key from Off to Start several times and get nothing. No sound, no clicking, no nothing. Get it towed home, wait until after dinner and go out and try the key--maybe a heat-soaked starter is part of my problem. Turn the key to Start and get nothing.

1. New Die Hard installed the previous week.
2. New ignition harness installed two years ago.
3. All ground straps in place.

Questions:

Could a failed starter solenoid cause the engine to quit?
Could a bad condenser do that?