as I understood the situation, your squids DON’T REQUIRE authentication of the users to accept connections for proxiing, but your internal website is which requires users to be authenticated to use some service.
If this is true, I think there might be a change in the url pointing to the website (https://… instead of http://…). Then there are two possibilities:
(1) squid is not configured to listen for/handle ssl connections;
(2) proxie configuration in your browsers directs ssl requests not to the port whwre squids expect your requests.
Of course, if my assumption is wrong, the problem could be quite different.