2 things:
if you are turning wireless security on, this could be via using a 'WEP key' that is being used & therefore any device that wants to connect will need to know that WEP key
the 'PS2' mouse that you bought is more than likely a 'PS2' connector as opposed to a PS2 games console mouse, which is an older style mouse connection on PCs, they're normally a 'USB' connection now, however, mice also quite often come with an adaptor that lets you plug a PS2 (the PC port not the games console) not connection mouse into a USB port
finally:
step away from the computer