Try to manually unistall your DVD-RW drive by going to "Control panel" in your start up menu and choose classic menu style. Then double click on "Device manager" and it'll bring up a big list of hardware installed in your computer. Open or browse your drive and double click on your DVD-RW icon logo which will bring up it's statistics on that drive. It is a summary of how or if not your DVD-RW is working well or installed correctly. Unistall it by clicking on the "Driver" tab in the menu grid. Unistall the device and restart your computer. Next time you run your computer it will automatically detect your DVD-RW drive and install it brand new again. Insert a disc to see if it worked. If not, you may have internal problems in your computer and may need a technician to repair or install a new drive. Helps if you have warranty otherwise a new DVD-RW drive (depending on your computer) should be about 40-50$ shipped by your computers manufacture.
A similar thing happened to me with my DVD drive. Sometimes they just collapse, like hard drives. I needed to replace mine. I had an old computer with a perfect working DVD drive.