The first problem that I see is that you only have 192Mb of ram and are running windows xp. Windows xp is crippled by so little ram and your ability to burn is doubly cripled by so little ram. If you have a legit copy of win 98, you might want to consider a dual boot system as you might be able to do it under win 98.
I'm guessing that your 80 gig hard drive is pretty much full. you need lots of space to deal with dvd's (6-14 gig free space). Usally if you have 10 gig free you can do most common things.
Plenty of people burn just fine on a pentium 3 (your probably pushing it but there is no reason you cannot do it).
Another thing to look at is your ide controler (this is the device that controls your drive). If you have a pentium 3, its quite possible that that it has a controler that cannot do fast enough speed for dvd burning. Actually it just limits the speed you can burn at, but forcing high speed dvd media to burn slower often ends in bad burns or disaster. So you might have to look for certain medias.
Increasing you ram would be a good idea, but you ram is so outdated, you could probably buy another motherboard, new style ram and pay for a little bit of a new cpu for the cost of the the older ram. They know sdram is outdated, and hard to find and they rape you on the price.
Could you give more specific info on your system (and maybe ability to upgrade, how much you can spend).
I'll tell you, you can probably do dvd burning (most aspects of it). I have heard of it hapening on old systems like that plenty of times. It might/will cause restrictions and problems though. You might want to see if you can get some used ram locally at computer shops (you can sometimes find it really cheap but it might not be tested and is a gamble). You might even be able to buy a low end computer used (I have seen old used pentium 3 systems for under 100$ and you can gut the ram and whatever else). New sdram is not worth buying. It is so expensive (because it is so obsolete), that you could upgrade to beter equipment and new ram and be beter off.
I'm sure others can provide more info, but should you try a new drive with your computer (it may or may not work, plenty have done it on low systems like that, it depends on your equipment), if it doesn't work, you can update your system, and the drive will work with a newer system. Are you using this old system becuse its what you can afford, or because it hapens to be what you have?
Also, how comfortable are you poking around the inside of your computer and how much do you know?