Shutdown issue, could be overheating or a failing motherboard. The issue with browsers, when was the last time you did a clean Windows setup on it? Maybe time to do that. But since it's shutting down on you, you first need to either fix that, likely with a replacement motherboard, or replace the system. Looks like that thing has a Celeron CPU and DDR2 RAM, that is no good for modern use, you can buy a used $100-150 laptop that is much faster and works. I like the Lenovo T420 or 430 models in that price range.