The first thing to do is check for any button on your keyboard which has an icon that looks like a touchpad with a line through it. Press it and see if the cursor starts moving again. ... But in most cases, you'll need to press and hold the Fn key and then press the relevant function key to bring your cursor back to life.
Too much going on in the background ? May take a while for the mouse movement to have it's turn with the resources. Could try closing down stuff. Use Task Manager to check what's running and hogging stuff.
It's harmless to change the battery but don't throw the old one away. I always use rechargeables in my mice, so it's easy to change and then recharge the old one.
Another possibility is interference; have you moved the laptop recently? Try in in a different location.
The problem may be due to numerous mouse drivers or outdated drivers on your PC. If your cursor sticks or disappears, you should go to the Device Manager and check for mouse drivers and update them.