Mouse Acting On Its Own

you said you don't have a keyboard attached, but try this anyway.

install Yet Another Key Displayer and see if the little box that displays the keys pressed keeps displaying something even when you're not pressing any keys. in my case it kept displaying "LShift, OemClear"
if it does then continue to the next step, if not, then sorry that I couldn't help you.

install SharpKeys and click Add, that'll open a window with 2 lists and each of them has a button named "Type Key", click the button below the left list and that'll open a window.
after a few seconds it should automatically type the key that's causing you problems. emphasis on should because I never met anyone else with this bug and I don't know if this will work for other people or not.
click Ok.
on the right list, scroll down and select "Num 5: (00_4C)", this is the Clear key, which does nothing unless you have numlock enabled as far as I know.
click Ok > Write to Registry > reboot your computer

check if that fixes your problem.
you can also try disabling the problem key by selecting "-- Turn Key Off (00_00)" on the right list, or setting it to one of the "Unknown" keys, but in my case that didn't fix the bug, only remapping it to Clear worked.
the side effect is that if you enable numlock, it'll automatically press 5 every 2 seconds, I hope that doesn't bother you much.