Its rare to have a dud wireless mouse.
There's a good chance that both these computers are running Windows, yes? Windows tries to load any software called "drivers" related to whatever you're plugging in. At times, it also tries to connect to the internet to find updated drivers so that the device works as intended, to the best it can.
Leave it plugged in for a while and try it after some time has passed. It might just be a case of it not getting "installed" with the computer. That's my best guess.