Hi, dschenk. Premiere Elements has its own forum and you'll get better help with video questions there. I'll move this for you.
First, did you use Premiere Elements' Video Importer to get the video files from the DVD to your computer? If not, you should. It will save you trouble later on. Put the DVD in your computer's disc drive and use Add Media/From PC DVD or DVD Camera to rip the video files to your computer.
Second, after you load the file into your video project, you must wait for Premiere Elements to conform it before you start editing it. If your sound cuts off partway through, it's because you didn't let the program fully conform the audio. Clear the file from your project and wait for the program to fully conform the file. You can see the progress along the bottom left and right of the program's interface.
Throw away what you've done so far and start over, using those steps and your project should edit just fine.
Welcome to the forum, and thanks to Barbara B. for moving the post here.
When you say "I am trying to edit an old homemade DVD that used VOB files. " I wonder if you are having issues with the first VOB, which can also contain Menus and navigation info, along with the MPEG-2 material, which can span several VOB's. Some software, and most DVR's write the first VOB out of the DVD-specs., and those create problems. See this article: http://forums.adobe.com/message/2298534#2298534 for more details, along with Steve's suggestions.