To clean out the DVD drive (for slot drives) just get a compressed air can that has one of those straw like tube with it. Then just blow out (toward the Earth direction). You also can go to any book electronic store and buy a cheap CD/DVD cleaning disk too.
Now go to /Applications/Utilities/System Profiler and launch it. then in it select "Disk Burning" to see if the Mac still sees the drive.
Mac Pro Dual 2.8 Quad (2nd gen), 14G Ram, Two DVD-RW Drives, OS X 10.9.1
2006 Mac Book Pro 2.16 (first Gen) OS X 10.7.5
2TB Time Capsule, 2 TB
32G iPhone 4S Black, iPad (3rd Gen) 32G Black