Hi and welcome to the forum, make21!
It looks as your burner and the media don't like each other. An update on the firmware might solve it - but I doubt it. The burner is a rather old model.
I 19:37:32 Destination Device: [1:0:0] HP DVD Writer 640c ES04 (E:) (ATA)
http://forum.rpc1.org/dl_firmware.php?download_id=2034
If you update
1. No disc in the burner
2. All other programs closed
3. They tray closed