1972 duster weak power

I've been forced to take out the Duster in cold weather, and has trouble starting. First the radio comes on and off as it pleases, but that never stopped the car from starting. When I turn the key the motor turns fast like it should , I have fuel pumping fine and the carb is tuned properly. At first I thought it was carb issue spitting and shuddering, but I put my carb on my Dart and the thing started up with no issue! Now here's the weird part, when I put my key in the dome light is dim, the door buzzer seldomly goes on and the radio seldomly turns on when key is turned a click. BUT, when the buzzer goes on , the dome gets brighter and radio turns on, VOILA!! The car starts. ... There's a short somewhere, but all the wires look fine except on the back of the Alt. Gauge in the dash, the negative wire is clean and the positve post was HOT and covered with surface rust. ... On a side note, when the car is off, the dome is dim and it struggles with the headlights going on and are very dim. I have a new Alt, voltage regulator, and battery. .. is there something important I'm missing here???

not a short but a poor connection(s) somewhere. I'd start by cleaning the bulkhead terminals (both halves) and batt cables/posts (including the neg ground path)

Wouldn't hurt to bypass the ammeter for a bit, and put a voltmeter on pos wire at batt and see where it's at for test purposes. And of course, do as suggested, to check for good non-burnt contact at bulkhead and other connecting locations.

The main hot/red wire going through the bulkhead connector is probably the culprit (I've been there, done that). The connection at the firewall will corrode, then overheat, then melt the terminal block. It could be causing the strain on your gauge also. The sooner you take care of this, the less damage you'll have.

"all the wires look fine except on the back of the Alt. Gauge in the dash, "

This is where I would start.

Again wires look clean, connections were all cleaned up and scuffed. Still the same issue. Though the car breifly had the buzzer going and dome brighter, radio still was not coming on BUT the car started with no hesitation on the first turn! Aaaand then after it warmed up it ran rougher. When put into gear, it stalled, dome light went very dim as well as the headlights. It took a couple turns, but I was able to restart the car. This time in gear, my Stock everything slant six sounded like it was cammed up or playing the entrance to "Hot For Teacher". When I tried giving it more gas, it sounded like I was deflating a pinched baloon!!! The car was running smoother just moments ago!!!... Am I not getting proper spark ? Coil, cap, rotor, wires, plugs, are all 3,000miles old. I've converted my original wiring harness to properly power a stock electronic ignition set up. And I tripled checked all of my spliced together wires to make sure they are secure

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Now here's the weird part, when I put my key in the dome light is dim, the door buzzer seldomly goes on and the radio seldomly turns on when key is turned a click. BUT, when the buzzer goes on , the dome gets brighter and radio turns on, VOILA!! The car starts.

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You might go thru & recheck that circuit since when it's "on" it cranks/start OK. Next I'd make up a bunch of jumper wires with alligator clips & jump fire directly to the coil/ECU & maybe from dist to ECU & to the "ign" terminal on the starter relay & ground the "grn" terminal on the starter relay & check the ground paths. Other than the cranking it might be as simple as a bad ECU.