Hey guys, thanks in advance for any help you can offer.

Last night I was driving and after about 30 minutes my dash lights began to dim. The dimmer switch still worked but bright was not bright. Then I noticed my turn signals stopped working and gauges were barely working. Next my headlights/tailights got very dim and then shut off (within 10 minutes). My wife was behind me in a big suv so that was some help with the light. The vette began to backfire badly and started shaking like it was about to die.

I pulled over and shut off the lights - even though they were out - the engine idled back to normal. After a few minutes I tried the lights again and they worked but were dim - then went out again.

Luckily I made it home and didn't have to leave the vette on the side of the road.

I'm not sure where to start. The alternator and battery are new. Is there a headlight/dash relay that can go out and draw too much current?

New alternators can be faulty out of the box. I'd start with a test to see if it's charging. Go to the battery next, new doesn't always mean functional. If your troubles started after the 2 new pieces, it's a good bet one of them is the culprit.
Let us know what you find and we'll go from there.

Yup,
Sounds like an alternater to me. If the car started missing along with the lights slowly dimming, then that means that there isn't enough voltage being supplied to the charging system. The alternater probably puked then the battery alone cannot keep up with the demand of the system.
That's my .02 cents
Sarge

IF the alternator is working, you have bad connections. It is not charging.

If you have access to a volt meter, with the engine running you should have 13 to 14 volts across the battery. If 12 or less, you're not charging.

Great. Thanks guys. I'll check the alternator. That sounds much better than what I expected.

My wife came home from church last sunday,and came in the house crying that her car just barely made it into the garage.she said all her lights and radio and heater went out on the way home,then all the idiot lights came on and flashed,its a 96 Olds cutlass,I asked her what the volt meter said b-4 it died,she said about 10 volts "why"?.after about 3 hours and $140.00 later it was running like a top again what a P.I.T.A. that was to change,I'll never complain about working on the Vettes engine again,at least you can see what you are doing under my hood and get to things. any way your problem sounds exactly like hers,ALTERNATOR check it out.