The plot thickens ...
I went out and bought an external DVD drive. I plugged it in, installed the driver and presto! I made a DVD in 3 minutes 15 seconds instead of 3 days 15 hours. I was happy.
Then I tried to make a second DVD, and same thing. It was crawling along at 65K per second instead of 10MB per second, which is what it was doing only minutes earlier.
Now last night using the old DVD burner I managed to get one DVD burned rather quickly, so this appears to be a software problem and it appears to be intermittent.
I tried doing a system restore but I have never had any luck with that. Whenever I've tried system restore in the past it goes through this whole song and dance, takes forever to start up again and then says, "Sorry, system restore was unsuccessful. No files changed." Same thing today. I don't know if it's related to the DVD problem or not but I have this experience with pretty much any computer I've tried to do a system restore on.
So ... does anyone have any guesses?