Despite your topic, I doubt the the monitor is the problem.. Still, it would help if you gave us more information about the computer and monitor.. The make and model is necessary.. Is this a desktop, or are you referring to a laptop? Despite your statement, I'm guessing the "Mouse" doesn't actually get stuck, but the cursor/arrow on the screen stops moving,,,,,, is that a correct "guess"? What have you tried to fix the problem? The more information you give us, the better informed our answer will be.
In the meantime, have you tried starting the computer into Safe Mode? If not, follow the steps in the link below to do so.. Does the mouse arrow work correctly in Safe Mode?
How To Start In 'Safe Mode'
Have you tried using a different mouse, and if possible, make it a PS2 mouse (round jack on the back of the computer), instead of a USB mouse???
Can you login using the keys on the keyboard? (Pressing the "tab" key will change the active location from one spot to the next, where you should be able to type in your username and password, then press the "Enter" key.)
Hope this helps and let us know more.
I can't sign in as my mouse is stuck at the the sign in on the welcome screen no matter what I do! HELP