Welcome to the site hosejockey.
First of all, does the dvd you’ve made in DVDFlick work on the computer? If you don’t have software for playing dvd files on the computer, try VLC, which is free to download and use: www.videolan.org
If that checks out, you can move on to problems with the drive or an incompatibility with your choice of media. Look in my signature and click on the guide for checking DMA by Womble. Make sure the dvd drive is in Ultra DMA mode (probably UDMA 2 for this drive, though it could be UDMA4). The most important part to look for is Current Transfer Mode.
If that is not a problem, you may have disks that are not recognized by this particular burner. What type are you using now? We recommend Verbatim 16x as a safe choice for most burners, though if you cannot find them, Sony disks are generally ok.
Burn at a moderate speed. For the Verbatims, 8x or 12x should be fine. For lesser quality disks, I’d try 8x.