That is indeed VERY strange. The first thing that I would do is Virus scan the hell out of it!
The next thing, is back up all the data, and then rebuild.
There has to be something pretty fundamentally wrong with it. Normally I would suggest a change of Mouse/Keyboard etc. But this sounds too “spookey”.
I know this is probably not what you wnated to hear, but I think that this is the best bet.