Strange issue when starting - smoke from under dash
 

Having an issue with my son's '81 Camaro starting. It is barely turning over so I'm going to check the battery and cables, but the reason I haven't done that yet is that when I try to start it there is smoke coming from under the dash, in the center, right behind the radio. I thought I smelled something burning as well. The smoke starts to come out after only 2 seconds of trying to start the car. Really odd. Any ideas? Thanks.

I would check the heater control and cigar lighter. Make sure both are off or unplugged.

Sounds like either a short in some old wiring, or possibly a ignition switch failing. The ignition switch is on the steering column near the brake pedal, so smoke could be rising from there.
I would get someone to watch under the dash with a flashlight as you turn the key. Maybe they can see where the smoke is coming from at that time. I would also keep an extinguisher handy, so you don't burn the car down during troubleshooting!

This is not uncommon on older cars, especially British cars, where the outer wire casing cracks and lets the diagnostic smoke escape from inside. Once you get the wiring fixed, be sure to reinsert new wire smoke (Lucas makes install kits for this), so that you'll be able to find the next problem should you have one.
lol, ok seriously tho, the only way to see where the smoke signals are coming from is to do what Vall said and have someone under the dash watching for it, unless if you're very limber then you can DIY.

Well there's a vent/duct right near the radio and the smoke seems to be coming from there. What's odd is I was able to jump start the car just fine, and there was no smoke when I jump started it. I let the car run for awhile, shut it off, made sure the battery had a full charge, then tried to start it again and it would barely turn over, and I got smoke again. So I have two problems, she won't start and smokes when I try, and they seem to be related. I guess the battery could be bad since my charger won't tell me if it's bad or not so I'll try replacing it, but not sure why it's smoking.

low voltage could be forcing a relay to engage partly and its smoking. how much smoke are we talking about, very light and not easily noticed or heavy smoke signal.

Very good point! If the car has a low voltage scenario, all the amperages, and resistance will go up. If it doesn't do it with a jump, then get the battery tested. But I'd still be concerned with the smoke, and whether there's been damage done now, that might create an issue again after a good battery is installed.

Lucas Electric=Prince of Darkness! A bit of British humor.

It's just a small amount of wispy smoke, definitely noticeable, but not filling the car with smoke or anything like that.

Thanks to everyone for the replies. Screwed up my back and haven't been able to work on it further, but I will as soon as my back allows.

Swapped in a different battery and it started right up without any of the smoke. Weird.

i had a similar isue in my car and i had the power wire for my guage set ground out on top of the column at some point it fell out of the retainers and rubbed on a sharp spot of the mount took forever to find