I'm a big proponent of building your own rig since it can save you a bunch of money and you're able to get precisely that parts you want. Now, it's not the case that building your own will always
be cheaper than buying one off the shelf with similar specs, but in my experience it usually is.
For example, last month I built myself a brand new computer. Like you, my old computer was about five years old and also like you I was looking for a machine that could handle the latest games (you can read my forum discussion about it here
.) As you can see I got a kickass computer for a little over $1,000 on Newegg. Add in the prices of Windows 7 OEM, an aftermarket heatsink/fan and a Creative Soundblaster OEM sound card and the final cost was something like $1,200.
I did a quick search on Dell's website (for example) and the closest machine they have for sale that I saw is this one
which is on sale for $1,800. The most comparable desktop on Newegg runs about $1,600
In the end it comes down to preference. I prefer to build my own because, well, I like to build PCs. You may not like to do it. Neither of us is wrong, of course. The decision to build or buy is like picking out underwear: some people like boxers, others like briefs, and still others prefer something else altogether. If you're a briefs wearer, then here's a very decently spec'd rig for $950