I don't know what happened here but now I have Local Area Connection (Cisco VPN), Local Area Connection 2 (TAP Windows Adapter V9), Local Area Connection 3 (TAP-WIN32 Adapter OS), Local Area Connection 4 (TAP Windows Adapter V9 #2). There was only two before - one for Parallels and one for VPN. I can't connect to any network now, bridged or shared - wired or wireless, regardless of what I try. I've tried reinstalling parallel tools twice now and nothing. Of course I just arrived on site at a project 2 hours away and have no way to do the work I was sent here to do.
Looking over that KB post, I had already tried 1-4. Restore network settings seems to have worked. Thanks. I'd still love to know why I have all these additional network adapters in network Connections that weren't there before. Local Area Connection 2 (TAP Windows Adapter V9), Local Area Connection 3 (TAP-WIN32 Adapter OS), Local Area Connection 4 (TAP Windows Adapter V9 #2).