Hi There!
I have the kind of same problem,
My vSphere vCenter Infrastructure is:
- One SQL Server VM (windows 2008 R2)
- One SSO Server VM (windows 2008 R2)
- One vCenter Server with Inventory Services and Web Client Server (windows 2008 R2)
My situation today I try to log-in to my vCenter Web Client and show me the message "To get started, either install a vCenter Server, or obtain access permission to an existing vCenter Server system." but the weird thing is that I can use the Windows vSphere Client and all the permissions are OK, I have permissions at Domain level, I've tried to log-in with admin@system-domain -> not work, administrator@mydomain.com -> not work, I've tried the following things:
1.- On web client: I went to "Administration" -> "SSO Users and Groups" -> "Groups tab" -> "__Administrators__" -> "Add Principals" -> add "admin@System-Domain" and restart the Web Client, it didn't work
2.- Re-install "Inventory Services" and "Web client" restart all vCenter infrastructure but it didn't work 
3.- Reconfigure SSO on my Web Client, using the client-repoint.bat; C:\Program Files\VMware\Infrastructure\vSphereWebClient\scripts\client-repoint.bat https://<my_SSO_IP>:7444/lookupservice/sdk admin my_sso_pass, but it didn't work
4.- Install a new Web Client on a different VM and pointing at existing SSO, it didn't work :'(
I have no Idea what more I can do, I think is a SSO problem but I don't know how to check it, I think SSO doesn't provide the vCenter information to the Web Client.
Any idea?
Please help me guys!