Welcome to the forums...good to see another Texan here.
When you convert to dvd-video format, you normally get a Video_TS folder (containing .vob, .ifo, and .bup files) and an empty Audio_TS folder. The Audio_TS folder is a legacy, not used, so there is nothing out of the ordinary going on with your conversions. DVD-Video has the video and audio streams combined in the .vob files.
I personally use a free program called ImgBurn to burn videos to disks. If you'd like to try it, you should read some guides at their forums on how to burn dvd-video with it. http://forum.imgburn.com/index.php?showforum=4
I looked up your burner through Google and it seems to date from late 2004 to early 2005. You might want to look for a firmware update for it, since many new types of media have come out since then that it may not recognize. The burner has to recognize the blank disks to know the exact burning strategy to apply, otherwise it will use a generic strategy that may not work well, if at all.
Another option is to use good media that has been around a long time. Verbatim 8x or 16x or Taiyo Yuden 8x +R disks would be my recommendation.
It seems the HP DVD630C was a rebadge of the BenQ 1620 drive (going on flimsy Google evidence). The 1620 drives were excellent while they ran. They were also notoriously fragile and many broke down quickly.
Another thing to check, while I have your attention :). Follow this guide to check DMA status for your burner: http://club.cdfreaks.com/f61/troubleshooting-enabling-checking-dma-windows-vista-xp-2000-me-9x-101616/ The important part to look for is Current Transfer Status. It should be Ultra DMA 2 for this drive.