I would look in the cmos settings to make sure the mouse port is turned on. If it is turned on, I would try using a known good mouse. I would also try using a usb mouse to verify the mother board.
You could consider buying a USB mouse in the meantime and plugging it into a free USB port. Though, if you can't shut down you will have to hard shut it off by pressing the power button before your computer recognizes the mouse.
Boot into Bios by pressing the f2 key right after turning on the computer and make sure it is enabled. If it is and doesnt show your mouse, it's damaged.
Double check and make sure that your mouse is functioning properly by inspecting cables and seeing if you mouse is clogged or just broken. It could be your motherboard.
Try the mouse on another computer to see that the mouse works. Try another mouse. Check the Bios that mouse is on. Look on the motherboard for loose solder connections.
First thing you want to do is go into the BIOS settings and make sure the PS2 mouse setting is on. If that doesn't work it could be your port is fried, so the next best and cheapest thing to do would be to buy a USB mouse.