The media it's referring to is the blank DVD in your disc drive. The program is not seeing it.
This can happen because either a) you don't have a disc in your disc drive, or b) because another another program (Nero is notorious for this) is blocking the program's access to your disc drive.
Try selecting the option to burn to a Folder on your hard drive.
1st, see if this works to write a DVD
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 write files or folders or ISO to disc for DVD or BluRay (send the author a PayPal donation if you like his program)
When you write to disc with Imgburn, use the SLOWEST possible speed setting, so your burner has the best chance to create "good, well formed" laser burn holes... since no DVD player is required to read a burned disc, having a "good" one from a high quality blank will help
2nd, troubleshooting steps
These notes are (mostly) for Encore, but since the disc burning module inside Premiere Elements is also licensed from Roxio, the steps and ideas are the same for PE
As well as the below, right click the program icon and select Run as Administrator, which is NOT the same thing as running the computer with the Administrator account, and which fixes several "odd" problems... To create a two layer DVD or a BluRay, you must have Encore set to use the Run as Administrator option
Run as Administrator http://forums.adobe.com/thread/969395
Odd Errors http://forums.adobe.com/thread/670174
Long File Names or odd characters cause problems
And This Message Thread http://forums.adobe.com/thread/665641
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
Last, The Help-and-Tutorials page http://forums.adobe.com/thread/1275830 may help
Just some supplementary questions
a. What version of Premiere Elements are you using and on what computer operating system is it running?
b. When you are in the burn dialog and your DVD disc is in the burner drive tray, what is the exact message for
Status? Is it as you wrote "No Media Available" or is it rather "Media Not Present"? A minor distinction but I just
want to make sure we are in the same place.
c. When you see the "No Media Available" in the Status field, have you clicked on the Rescan button in that burn dialog?
If so, can we assume that did not work to solve the problem?
Looking forward to further developments.