Yes, if it won't even play pre-recorded discs then there is likely something wrong with the drive.
The first thing I would do is turn off the computer, open up the case, and unplug and reseat the cables that attach to the drive, at both ends of the cables where possible.
If that doesn't change things, then I would swap the positions of the other CD-ROM and the burner (keeping in mind that you may need to adjust the master/slave jumpers if you don't have the devices set to cable-select). I would also try running with just the burner installed (in case there is some interference from another device on the bus).
If that doesn't change things, then I would check to see if the drive is still under warranty and can be repaired or exchanged.
If it isn't under warranty, or it is but you are feeling a little adventurous and don't mind voiding the warranty, I would suggest trying to clean the inside of the drive, in case some dust/dirt has settled on the laser lens assembly. You need to be careful doing this, since it could damage the drive irreparably if you do it badly (assuming it isn't already damaged irreparably).
Here is a post with links to some cleaning instructions (courtesy Inertia):
http://www.cdrlabs.com/phpBB/viewtopic. ... 0949#70949