So yesterday I found myself stuck at work because the car wouldn't start. I agreed with kingnutin's response that it sounded like the ignition switch. So I had my daughter come pick me up and I had her bring me some tools so that I could pull the ignition switch and take it home and check the connectors. While I was waiting for her I did some more searching and came across this great Sparky's Answers: 2003 Chevrolet Impala Security Light Flashes and The Engine Will Not Run
write-up about the ignition switch and lock. This write-up offers a good explanation and lots of pictures that makes it very easy to follow.
I followed the above write-up and pulled the ignition switch but then realized that I had left the windows down which wasn't going to be good as it was parked in a downtown parking garage. So I re-installed the ignition switch so that I could put the windows up. When I did this I decided to go ahead and check to see if it would start - and it cranked right up.
I decided to go ahead and try to drive it home, it was driving fine and I was headed down the freeway at 70mph and the gauges jumped up and down and the dashlights flicked and the engine died. I coasted to a stop on the side of the road and pondered what I was going to do next. While sitting there I rapped on the back of the ignition switch (that was still hanging out of the dash) and turned the key and it fired back up again.
When I got home I left the car running and tried the blinker...nothing, then I pushed on the black cover on the back of the ignition switch and the blinkers worked, if I let go they would stop.
I put in a new ignition switch and everything seems to be working fine. I'll update if the problems return.
Sorry for the long posts but while searching the internet for solutions I must have read 500 discussions about similar problems but only 1 or 2 bothered to update their posts with how they fixed the problem. Hopefully this will help someone else when the run into these problems.
Here's some pictures of the old switch, you can see the burned contacts. It's hard to see but the back contact in the right is also burned.: