You can check if the button on the front of the drive is sticking. Other than that, it may have gone bad. If it went bad, you'll just have to replace it.
You might also check the cable connection (both ends) to the drive inside the computer and any switches on the drive case inside the computer. There might even be a bad setting in the BIOS.
Try to remember when this problem started. Did you change or install/de-install anything on your computer just before the DVD problem started?
You can leave your games installed right where they are. Your DVD drive doesn't have anything to do with your installed games unless some of them are older games that require the DVD to be in the drive before they will play. Once you get the DVD drive issue fixed, then you can just play those games as usual. No need to uninstall anything.