What is the make/model of your computer?
So is this a laptop and you mean you plug in the A/C adapter which should power the laptop and charge the on-board battery but if you do it won't boot?
And why would a wireless mouse, plug into a USB port ... or is it a little transmitter that plugs in and that wirelessly connects to the mouse?
If two completely different style connections (A/C power and USB port) with completely different purposes cause the laptop to BSOD then I suspect it is a hardware problem, most likely power. Perhaps you installed a knock-off battery or have a knock-off power adapter; laptops can be quite temperamental when it comes to power.
If you boot the computer without the mouse tranmitter and then, once it is powered up, plug in the mouse transmitter, does it function properly or will it BSOD then?