OK, so what about installing the telnet client, netcat or curl and seeing if you can do some port connectivity tests:
nc -vv google.com 443
curl -v -k https://google.com
telnet google.com 443
Something like that, see if you can still talk https out. If that works, then pfft I dunno.
nc -vv google.com 443
curl -v -k https://google.com
telnet google.com 443
Something like that, see if you can still talk https out. If that works, then pfft I dunno.