Yes, your computer can easily handle an upgrade to a DVD burner.
This one for a mere $30 can do it.
No, unfortunately your CD RW burner can not do it.
So here's my recommendation.
Just swap your CD RW drive out for this guy.
You can't use the cheaper SATA drives unfortunately as your computer is too old and uses IDE cables.
So I selected an IDE drive for you.
(you can confirm this if you open up your computer and check and see if your cd rw drive has a ribbon cable on it)
IDE cables are the flat wide ribbon cables
SATA are much thinner and slimmer