Apparently a recent Windows Update broke OWA and RWW on SBS2008 server. I get notifications every 30min that the Microsoft Exchange Search Index service failed to start. (Try and start it manually, and you get an Error 1068 "The dependency service or group failed to start".) It is possible that other things are wrong, but this stands-out, and I don't know what else to check for.
Symptoms are that no browsers will access the OWA links /remote or /exchange. Using Chrome or Firefox gives the main login screen, but it will not authenticate; using IE does not even give the login screen.