The fastest way to test if a drive is reading a data disc is to use a boot CD. You can use anything really. Windows Installation CD, Universal Boot CD (
http://www.ultimatebootcd.com/) or Memtest (
http://www.memtest.org/). I recommend the Ultimate boot disc for test as this should boot without prompt if your BIOS is configured to boot to CD.
If the system will not boot to a CD, then check the BIOS. You usually can access it via F2 for Dell (I believe. Just watch the screen and it should tell you). The common BIOS access keys are F2, F1(with error) and the DEL key. There should be a top category for BOOT. Check to see that the first boot device is the optical drive. It should have an identifier indicating which is which. If it is a hard drive you may see WD(western digital) and some numbers. Chances are it is a Toshiba or Samsung drive. The optical drive should have something with CD or DVD in the identification.
If you have configured your BIOS to boot from CD and you are prompted and the system does not boot to the disc, then you have a bad drive. This test will eliminate the Windows aspect of the system and only uses BIOS information to boot. There is a chance that your BIOS has failed, but that is unusual and would cause more of a failure than just the optical drive failure.
If you cannot access the BIOS due to IT password, then you have to get the info from your IT department.