Strange, I can use the webbrowser for other sites with no problem at all, even https.
On same router (connected by cable as is the raspberry) connection with windows vista
and Linux and there I can easy connect to your https site., But there I use Firefox as browser.
Has it maybe some relation with certificates for your https site access?
The ethernet connection is made on a router connected to another router, maybe I can test tomorrow
with direct connection to the main router, to see if that makes any difference..