Assuming you have the necessary software, and the DVD ROM, they should play. You may get some 'lag', or it appears choppy as the processor speed isn't exactly great, but there's no reason why it shouldn't.
Also, your video card must be able to support certain video accelleration functions, and must have at least 8mb of RAM to play full screen.
reight click on desktop>properties>settings tab>advanced>adapter tab, all the information will be listed there!
chip type: s3 savage/mx dac type: s3 sdac memory size: 8mb adapter string: s3 compatible display adapter
Yes you can play dvd's but they are'nt going to play very smooth, you'll probably find half of the movies will be glitchy!
You CAN still watch them but they wont always play very smoothly! The way to get around this is to upgrade which may or may not appeal to you at the moment!
And by upgrade, he means you'll have to go to an entirely new laptop. Unfortunately, it's only be recent here where the graphics can be upgraded at all. Even then, you'd have to go to the company that made your laptop (or eBay possibly) to get the upgrade module because of how new it is. They are working to standardize this last I checked. If you already have the DVD player software, it'd be worth a shot to try and see if you notice it in the first place.
If you run it windowed it should play alright, just try and see, maybe fullscreen won't be as bad as the above reply's have said though they're usually spot on. A new laptop probably isn't realistic for you I imagine but I'd say you've got enough cooking under the hood to make for a decent experience.
Update your drivers, get a good dvd player (software) make sure the disk is in good shape, and you should be fine. I have a winbook XL2 and when it worked , it played dvd's flawless no lag. It has less memory, same vid memory, and a slower cpu, then what your running so you should be fine. BTW: I used power dvd, and don't run programs.