My iMac (Intel) doesn't recognize that it even has

Some of the intel imacs have a problem with their drives failing.

First thing to do is go to the apple menu then to about this mac and then click on more info once this has opened click on Disc Burning and this will give you the indication of whether the disk drive is still operating

If it is a system software problem what to do is go onto the apple website and go to support and download the latest system update but make sure it is the combo update i.e. for 10.5.8 it is named "Mac OS X 10.5.8 Combo Update" the reason for choosing this one is this update not only contains the System updater but also the Security Patches and other subsiduary files.

Hope this helps