Cannot use mouse anymore, cursor snaps back to fixed position on screen

Since a few days I am having a problem with my mouse. Everytime I move the mouse cursor it snaps back to a fixed position within a second. This behaviour makes it almost impossible to use the mouse.

This occured for the first time a few days ago, when I woke the iMac from sleep. The positions to where it snaps back has changed one time, also when I woke the iMac.

I use a mighty mouse, but this happens also with a different mouse. So it isn't related to the physical mouse, it has to be software related.

My iMac is password protected, so I get a login screen. At this point my mouse is already unusable, so I think it has something to do with the mouse driver software.

I have searched the web and these forums for a solution, but I couldn't find one.
So I hope that someone has a few tips where to look, or what to do, to get it working again.

Can someone give me some tips on how to operate the computer with the keyboard? For example, what key do you use to start a program from the applications folder? I've tried some combinations with enter and space but it can't get it to work. This would be help, maybe that way I can analyze the problem.

Thanks for any help that you can provide.
Jeroen

My iMac has the latest software updates applied