a 16"inch or 17 inch size mud and snow tire would do for that vehicle.

What kind of system are you talking about here? If it's shutting down while on AC power, then the first thing I would suspect is an overheated system. Check the interior of the system if it's a tower and make sure the cooling fins on the CPUs heat sink aren't choked with dust. Laptops CPUs are also susceptible to overheating and the most common cause is dust build-up on the exhaust side of the cooling fan. Cleaning this area usually requires disassembly of the laptop - canned air only makes the problem worse - so if you don't feel comfortable taking your laptop apart take it to a professional PC/laptop repair person.