We don't use the web client often, but we have a need for it now. It used to work fine. We get a certificate warning in IE, but when you click the "continue to this website" link, it just reloads the same page. I have the IP in my Trusted Sites. Google Chrome gives the certificate warning, but clicking "proceed anyway" brings up the main vSphere page and you can login and launch the web client. I've tried this on several machines with both IE8 and IE9. IE8 won't even bring up the security warning, the page won't load.
We're running ESXi 4.0.0, 228255. The cert is from the VMware installer and has not expired (valid through 2020).
Here are the ports that are open:
open port 80/tcp
open port 135/tcp
open port 139/tcp
open port 389/tcp
open port 443/tcp
open port 445/tcp
open port 1041/tcp
open port 1075/tcp
open port 1076/tcp
open port 1137/tcp
open port 3389/tcp
open port 8009/tcp
open port 8443/tcp
open port 9876/tcp
Thank you for taking a look.