Welcome to the forum.
One other possibility, along the lines of Steve's comments, could be bad blank media. What brand, and what type of blank media are you using?
I recommend Falcon Pro, Verbatim or Taiyo-Yuden blank media, and shun Memorex, TDK or Ritek (recent versions), and any "store brand," like Staples, Office Depot, or similar.
Also, a little tip: do not place the blank media into the multi-drive, before you launch the program. Wait until just before you start the Burn to Disc operation to load the blank media.
Please excuse any thing that you may have gone over already with your troubleshooting before you posted your thread, but just so that I do not take anything for granted:
a. When you are in the burn dialog is the name of your burner accurately listed and selected?
b. What brand and type of DVD disc are you inserting in the DVD/CD burner tray? Have you tried other discs in that batch or gotten a different brand or type to try? Can you use the same DVD/CD burner and brand/type disc for successful burn to disc if you are using a program other than Premiere Elements (perhaps a burn to DVD using Windows DVD Maker if it came with your operating system)?
c. Then the typical questions...what versions of Premiere Elements are you using? If you are having this problem with burn to disc, can you still burn to folder?
We will be watching for your follow up.
You MAY also have software installed that does not PE communicate with the drive... examples below
Things and Software to AVOID when authoring/burning a disc... says Encore, but also applies to Premiere Elements and disc burning
Start --> http://forums.adobe.com/thread/608660
#2 has WHY Explained http://forums.adobe.com/thread/607390
Set your DVD output to a folder on your hard drive and then use the FREE http://www.imgburn.com/index.php?act=download to the folder to disc for DVD or BluRay (send the author a PayPal donation if you like his program)
If writing to a folder and using Imgburn works, you may figure out your basic problem at your leisure