One other super basic thing that always causes issues like this - are you sure the date and time are properly set on your computer? SSL certificates are only valid during certain dates, and if your system date is way off to the point that your computer thinks the SSL certificates are not currently valid, it will cause lots of problems and the internet will basically be unusable.

Because of the proxy messages, I agree with the others that it is also a good idea to run security scans on your computer also to make sure you don't have anything malicious running, either.