For my 1979 Corvette the turn signals did not light up or blink and all dash lights went off.  Upon replacing the turn signal flasher, the turn signals lit up and blinked and all dash lights came on.  This information did not appear anywhere in the owner's manual or factor assembly manual so perhaps it is unique to the wiring in my car which doesn't look to be hacked and in original condition.

I have the same problem with my '81. I replaced all of the bulbs and the flasher on the fuse panel. Nothing. The hazards lights work, but nothing from the turn signals. The lights don't come on or blink. I've also got a horn that won't work. I replaced the fuse and the contacts under the button, but it still doesn't make any sound. I think the problem is in the steering column.

Any other thoughts?

I would agree that your issue is in the column. Most likely a break in the turn sig wiring harness....a pita to change.