An ongoing issue for some people who have installed Mountain Lion is the inability to access their systems' internal optical drives. Once installed, inserting a disc results in a couple of noises before the disc is ejected. While this can sometimes happen for burned discs that are no longer readable, it appears to happen for all discs, be they home-burned or commercial.
If this is happening on your system, first try testing the problem with multiple operating systems to see if the problem is hardware or software based. If your system came with gray boot discs, try inserting them and restarting with the C key held down to boot off of them. If successful then this is evidence enough that the drive is working.
If your system shipped with OS X Lion and no gray installation discs, then you can try booting to the Recovery HD partition by holding the Command-R keys at startup. When the OS X Tools load, click the option for Disk Utility and then try inserting a disc. If the drive properly reads it, then it should show up in the Disk Utility sidebar. In addition to using the current Recovery HD partition (which may be based on OS X 10.8 Mountain Lion), you can try booting to Internet Recovery by holding down Option-Command-R. For systems that were upgraded to Mountain Lion, this will load a version of the Recovery Drive that is based on OS X 10.7, avoiding any potential conflict from OS X 10.8.
Upon testing the drive, if you cannot get it to work in any of these alternate boot environments, you may need to have the drive serviced and replaced. Otherwise, there are several options you might attempt to get the drive working again.
The first is to simply boot your system to Safe Mode by holding the Shift key at startup. If the optical drive works only in this mode, you may need to check for and uninstall third-party software that might be contributing to the faulty behavior.
Since Safe Mode runs a few cache-cleaning routines and other maintenance tasks, sometimes just doing this is enough to spur the system into behaving properly when booted normally. However, you can also try some other OnyX to clear system and user cache files that, if corrupt, may contribute to odd system behaviors.to see if they help. These include resetting the system's SMC and PRAM hardware variables, and using an up-to-date maintenance utility such as
Additionally, you can try adjusting some settings such as the default handling of optical drives in the CDs & DVDs system preferences. Toggle the various options in this preferences pane to different values, then revert them to see if you can spur a difference in behavior.
Lastly, you can try reinstalling OS X to see if that helps the situation. If this problem happened only after updating Mountain Lion, then you can download and reapply the latest Combo updater for Mountain Lion (currently version 10.8.3) or you can boot to the OS X Recovery HD partition and try reinstalling Mountain Lion from there. Doing this will not affect your personal data and installed applications, but do be sure to back up before you make any major adjustments to the operating system. After reinstalling, see if the optical drive works on your first reboot (before applying any system updates), then try it again after applying any relevant updates.