So it looks like there may be some kind of driver (maybe some copy protection thing installed by a game?) or piece of software screwing around with your ability to read the discs you burn. There is a less drastic way to figure out if this is what is happening : download an ISO of one of those Linux live CDs, like Knoppix. Burn onto a CD with your GWA-4164B, then boot to the disc. Since windows does not get started, whatever interfering driver or software does not get loaded.
If the disc boots fine, it means your drive can indeed read CDs it burns and it is confirms it is some driver/software causing your pain. Then you probably should go ahead a do a clean Windows installation. If the disc won't boot, then it does mean something is wrong with the drive.
At least this way you can avoid reinstalling windows if you don't really need to.