Sorry for the delay, but life gets busy sometimes.
I tried cleaning the jets with a hanger, but I didn't have much luck. My wife came across a tip that suggested to pour some water down while flushing, and it flushed every time when we did that, so we decided to just get a new toilet. We put that in, much easier than I thought it would be when we started, and haven't had a problem since.
Thanks for all the help and info.