Um, I totally disagree that it's not worth building your own if you're not overclocking. I'm not OCing mine(I could, both my MoBo and CPU support it if I ever wanted to, I'd just need an aftermarket cooler instead of the stock), but I absolutely could not have bought anything actually worthwhile for what I spent building the PC I got last October.
Gaming PCs are expensive and filled with BS, but you can make a decent enough rig on the cheaper side without any extra flashy BS or ludicrous cost.
I spent about $750 and it would have been just over $500 if my old graphics card hadn't crapped itself, necessitating a new one.
Look at your current computer's components and figure out what you can reuse. Hard drives are usually pullable at least as storage, get a small SSD for your OS install and use that old platter monster for your files. Optical drives can almost always be scavenged, there's nothing fancy or exciting. Depending on type, size, and speed, possibly the RAM. Power supply no, MoBo no, CPU no, coming from a prebuilt you probably don't even have a graphics card.
Basically, don't buy **** you don't need. How big is your old monitor? Big enough? Right cables? Reuse that crap. You're here, your current keyboard and mouse are probably up to snuff.
I reused two hard drives, an optical drive, a replacement PSU I'd gotten my prebuilt, an old copy of Windows 7, my monitor, my keyboard/mouse, really cut down on expenses and I got a much better computer than I would have from a prebuilt.
Putting it together was basically ESD-prone Legos. A lot of stuff is obvious where it goes, and only goes in one way. Read everything. Your motherboard instructions. Your case instructions. The internet.
A note on graphics cards: Watch your case dimensions! Some of the more ridiculous graphics cards won't fit in some midtower cases.
Don't forget to ground yourself. Best practice is anti-static mats and an anti-static wristband, but you can get away with standing off carpet and grounding yourself to the metal parts of the case - Just keep a hand touching the case. I forgot to get a wristband when I built mine, so I just stood on the linoleum in the kitchen and ground myself on the metal. Leave things in their ESD bags until they go in, it protects them. (The laziest computer setup I've ever seen consisted of components lying on a sheet of plywood in ESD bags. This is not recommended ever, rofl.)
So yeah. It's doable. The first thing my computer did when I pushed the power button is beep to let me know it passed POST, then tried to load Windows from my old hard drive, which of course failed spectacularly. A quick trip to the BIOS and a CD in the drive got my Windows 7 install up and running on the SSD and my computer mostly working. My graphics card didn't quite make it, but it was older anyway so I just replaced it and all the crashing and rebooting the computer was doing in games the first day went right away.