Disconnect from all networks. Does it still happen? If it does, then it's not BB. Even the gov can't send information to a computer remotely if it's not connected to the internet.
Also, anybody with any remote sense of stealth is not going to RC a box when they can tell it's being used.
EDIT: @Thomasrutter has a good point. If it is someone trying to mess with you, it is extremely trivial to write a program that will move the mouse across the screen. This little C++ segment will do exactly what you are describing:
// loop forever, 1 will always equal 1
// generate random number between 0 and 100
random = Rand()%100;
// if the random number is greater than or equal to 75...
if(random >= 75)
// ...then generate random numbers and set the
// mouse coordinates to them
// pause for 10 seconds
// loop back to beginning
If that is the case, then open Task Manager (CTRL+ALT+DELETE) and check for any suspicious looking processes (such as
prank.exe or duplicate entries of legitimate processes)
Also, if you suspect this, check your startup folder (
Start -> All Programs -> Startup) for suspicious looking entries.
This kind of attack is unlikely, unless you know a programmer with a sense of humor, but that would definitely explain the kind of behavior you're describing. (I did this to one of my friends once :)