I have good news and bad news for you
First the good news: Yes, this is possible with a PC. In fact, it's free if you just want to have two users. Userful's Desktop Multiplier lets you do exactly what you're asking about: Plug in two monitors, keyboards, and mice, and two different people can use a single PC as if they were each using their own computer. In fact, Desktop Multiplier can scale up to supporting 10 users at the same time, if you have enough video cards. (If this sounds familiar, be careful: This is not the same as using one monitor/keyboard/mouse to control multiple computers. That requires a wholly different solution involving a KVM switch, a commonly available product.)
Now the bad news: It only runs on Linux, and there's nothing like this that I've ever seen for Windows. Are you willing to install an entirely new operating system just to be able to allow two users on the machine at the same time? If so, check out the Desktop Server version of Linux, which includes Desktop Multiplier as part of the default installation.
Is it worth it? I have to admit the technology sounds elegant and appealing, but with new PCs available for $399 or even $299 (and used ones even cheaper), what's the point? You're already going to have to buy another monitor... why not just set up a second, super-cheap PC that can be used for web browsing, light word processing, and the like. Two PCs also makes for a neat solution for doing data backups, as you can sync your files between the two computers.
Sorry it's probably not the answer you were looking for, but I hope it's helpful nonetheless.