Buying a computer is a big deal for a lot of people, and understandably so. For most people, their computer is a central part of their lives - both at work and at home. Because of this, you should make an educated decision on your computer purchase.
If you are a high-end user and speed is critical, I usually recommend buying the computer model that is one step down from the top-of-the-line model. This is often the best value. Manufacturers often charge a premium for their top model, which may only be slightly faster than the next model down.
If you just need to get a computer that allows you to browse the Web, send e-mail, and write documents, you don't need the best thing out there. However, don't short-change yourself by getting a old model or a generic computer. Try to get something that has been recently introduced, but isn't the fastest in its class. It will probably be faster than old top-of-the-line models, since the internal architecture may be faster. Also, make sure it is upgradable, so you can easily add more RAM, a larger hard drive, and a faster processor if you ever need to. Buying a generic model may seem like a good deal, but non-brand-name computers are much more prone to have hardware problems and issues with device drivers. These problems seldom justify the difference in cost. Do yourself a favor and spend a little extra to get a quality computer.
One more thing that I would recommend is that you buy a computer with as little RAM as possible. That's right -- the less, the better. Then, buy a RAM upgrade separately, since it is important to have a lot of RAM. Buying the RAM separately will typically save you a great deal of money since manufacturers charge the highest price possible for the RAM the include with or add to your computer purchase. You can usually find RAM on the Internet for roughly a third of the price.
was going to recommend a Gateway (Acer) brand Core i3 notebook computer, but then I re-read your question and you list one of the primary uses as DVD burning. That, and your current system is 8 years old. That's pretty good, but it's unusual for a retail purchased system. I think what you need to do is build your own. HOWEVER, it is never a good idea to re-use a power supply.