I killed my 64 Dart GT Convertible.

That starter relay won't actuate unless the NSS terminal is grounded, preferably thru the NSS at the transmission. However, I understand that some manual shift cars had a neutral switch wired differently, though the wiring diagram doesn't show that. Is your's manual? If so, insure it is in Park, ground the NSS terminal and see if the starter turns. Don't stand if front of the car in case it is not in neutral.

Re the two wires to the starter. The big red one is +12 V power and is always hot. The brown wire is what the starter relay puts +12 V on and goes to the starter solenoid. That is the part that makes the big "klunk" when the contacts engage. You can get a remote starter switch to actuate the starter under the hood. You connect it between +12 V and the terminal where the yellow wire goes. If that doesn't work, connect it to the brown wire, but be careful because that bypasses the NSS safety feature, so the car might jump forward when the starter turns.

I don't know how you lost the rear lights and turn signals. Check the fuses. Don't just look at them, test for <10 ohms w/ a multi-meter.