What kind of mouse? If it is cordless, it has only been fairly recently that cordless mice have come into their own for FPS style gaming.
If it's not that, there are a lot of things to consider, first off, though, it looks like your PC might be a bit underpowered for the games you're playing. You have a good graphics card, plenty of ram, but what speed is the CPU? Doom 3 is beyond bleeding edge graphics, and that means if you don't have some serious hardware, you'll suffer with lag. And you may suffer with some lag even with the most modern hardware. Doom 3 is that tough on a system.
Farcry is another top notch graphical game, and is often used for benchmarking systems for this reason.
All this said, there could be other things causing this problem, so I'll give a list of things I'd check:
First: Open up msconfig, (Start, run, type msconfig), and go to the Startup page. Do some serious housecleaning in there! Disable anything that isn't absolutely critical for you! If you have Realplayer installed, it does NOT need to have it's little applet in there to run when needed, so remove it! Same for Quicktime, AOL, Winamp, etcetera. I personally do not run ANY tray programs save my keyboard configuration applet, and my Antivirus...no video card tools in my tray, no NOTHING in my tray save those).
Second: Scope out your mouse. If it isn't a newer optical style mouse, (if it has no ball underneath, instead has a little light, you may be okay), consider getting one. They are far more accurate and responsive for gameplay. Consider a quality mouse, either a Microsoft, Logitech would be good. I wouldn't go cordless, but if you do, don't get less than a Logitech MX700, which was the first mouse Tom's Hardware Guide pronounced 'Fit for Gaming' when it comes to FPS lag. (I have one, and they're right, MX700 is a great mouse, but you could do as well with a far less expensive corded mouse).
Increase the sensitivity of your mouse in the Control Panel, under Printers and Other Hardware you'll find the applet for controlling your mouse.
If you are using the drivers that came with your mouse, you can try using generic drivers that ship with Windows, I've seen a few mouse drivers from manufacturers that weren't all that great, but the mice typically perform flawlessly with stock Windows drivers, so that's a thing you might look into.
See if this stuff gets you anywhere for starters. Luck!