How do I know if I have a DVD reader on my PC?

You're not the first person to be a bit baffled by how Microsoft Windows XP hides your hardware configuration details, but there are a couple of ways you can try and figure out whether your lack of DVD capabilities is a problem or just a non-DVD compatible drive. The easiest is to simply open up START -> Settings -> Control Panels -> System:

Then you'll want to click on the Hardware tab, at which point you'll see this:

As you might expect from the descriptions, you'll now want to click on Device Manager and then wait a few seconds while it launches:

I have opened up the "DVD/CD-ROM drives" area by clicking on the tiny "+" icon adjacent. Hopefully you'll see something called "DVD" or with "DVD" in its name, as I do on this PC which has both a CD burner and a DVD reader installed.

Double click on the individual hardware device you want to learn more about and you'll get a quick summary of its capabilities and featureset:

Notice carefully the text in the middle box to ensure it indicates it's all functioning correctly. You want to see "This device is working properly" as demonstrated here.

Oh, while you're here you can also check that you have your DVD player set to the correct region for movie playback too:

That answers your question of how to ascertain if you have a DVD drive, but the bigger question of why you can't watch movies, well, if you do have the DVD drive and can't get it to work, that's probably something else and your first step would be to test out the DVD in question in someone else's PC to make sure that it's PC compatible.