One of my customers had a similar kind of problem. If he was typing in the browser, whether it was email, facebook, or anything else, he kept having dropped characters. Anything he did outside of the internet browser worked fine.
This was a brand new computer, lots of memory, lots of disk space, and according to the performance monitor had lots of resources free and the CPU barely being used.
I swapped the keyboard, no change. I uninstalled the browser and reinstalled, no change. I tried various other things and had no joy.
Finally I loaded a different browser. He had been using Internet Explorer (version 7 at that time, I think) and I installed Firefox and made that his default browser. And that fixed it.
My best guess is that particular version of IE conflicted somehow with something else in the system (this was a fairly high-end Dell system). When IE wasn't running, no problem. I always suspected that if I had reloaded the OS (Windows Vista) without the various extra bits Dell put on there it would have solved the problem, but the customer was ok with using Firefox, and that was much less work.
However, later I tried IE 8 on the same system and it worked fine. By that time the customer was used to Firefox so I didn't switch him back.
So you might try a different browser.
