danandrews,
I'm using a URL of the form https://vCenterhostname:9443/vsphere-client
I tried adding a /# to make it look more like you example, but that didn't help. By the way, this URL works fine for other people in my office.
André,
I checked my proxy settings in IE and discovered, to my surprise, that a proxy was set. I turned it off and now I can access the web client!
Thanks for your help!