Run an optical drive benchmark.
Nero Toolkit - CD-DVD Speed + InfoTool or DVDInfo Pro.
See if the problem is limited to only DVDs as opposed to CDs.
Well, the drive isn't actually functional when it's doing this. I put the disc into the drive, it immediately starts to spin up and start reading the disc non-stop. I can't even access it or do anything else with it because it's reading the disc, but not actually doing anything. I think it might have something to do with Windows 7 and the annoying way it insists on reading the contents of everything on discs. Is there a way to shut that off?