If you have no keyboard installed, you shouldn't have keypresses.
Disconnect all peripherals, ALL OF THEM (check every USB and PS/2 port! for dongles, etc), even your Internet connection, no wifi, no Bluetooth, nothing, just a power cord, the tower, and the monitor, and see if it continues. If it does, try a different monitor (a TV over HDMI, maybe?) to rule out the monitor, too. The suspicion is that something (Internet, USB accessory) is somehow passing keystrokes, either by accident or by malice, and if it goes away with only a monitor connected, then you start looking for nasties. If it does keep doing keystrokes with only monitor and box connected, try booting to a Linux LiveCD/DVD to rule out the Windows installation itself. If you boot to a different monitor and a LiveCD and it is still passing keystrokes, then it's something inside your computer, either a hardware bug or one of your internal cards.
--Patrick