Question: Specific websites won’t work unless through proxy
Answer 1: Use Fiddler, run a session while you browse to a problematic site from a computer that doesn’t have the problem. Then do the same thing from a computer that does, both without a proxy and then a second session with a proxy. Compare the successes with the failures to see what’s different.
Answer 2: change the DNS to a specific local DNS server, rather than ‘getting automatically from ISP’. You might not have the same problem, in which case this won’t help, but the steps to solve my problem were:
Look up a local DNS server (or two)
Log-on to your router
Change the “Domain Name Server (DNS) Address” from “Get Automatically From ISP” to the address(es) you found