Well, I jumped the gun. I saw the post that was referenced during This Week on Channel 9 and I thought it would solve my problems. It did not. I still cannot open a VS 2008 solution from explorer.
My issue does seem to be that I have the UAC turned on. In order for VS 2008 to open cleanly, I have to run it as Administrator. If I don't, I get this message when I try to open a web project.
This means that I must always run VS 2008 as Administrator. I've updated the shortcut's compatibility settings so that I don't have to explicitly choose to run as admin though, because that got old very quickly.
When I double-click on a solution file that should open in VS 2008, I get nothing. Even after checking my solution files per Andrew Arnott's post. My solution files were just fine. If I run explorer as Administrator, and then double-click on the solution files, they open just fine. So permissions are my issue. I might just set my .sln file type to always open in VS 2008. When at home (where I have this problem), I'm typically working in 2008. If I need to open a pre-2008 solution, I can start up devenv first.