Fixed the oven!
Today, I fixed our gas oven. Here is the symptoms we were seeing:
0. The oven would only partially warm up.
1. The oven wouldn't turn on reliably.
2. If we re-plugged it in, it would sometimes work.
After some googling ("gas oven won't warm up all the way"), I found that it was most likely the ignitor in the oven. This was a useful link. I read that after around 7 years the ignitors tend to reach the end of their life, and I was reasonably sure that our oven was about that old.
The next step was to find the replacement part. It was roughly \$20.00 on Amazon. The hardest part was finding the part number. To do this, I had to find the model number of the stove. On our Frigidaire Gallery gas oven, it was behind the broiler drawer, visible when you open it. This was probably the hardest part of the whole thing! After I found the model number, I searched for the part number on Google. Once I had the part number, I found it on Amazon, and bought it.
The replacement was a breeze. Take out the oven racks, and the screws holding in the pans at the bottom of the oven. Then you can see the ignitor, and it is easily accessible once you remove a few more parts. The ignitor came with some basic instructions.
Much cheaper than paying a repair man \$200 bucks.