Possibly some interference from mods? You seem to have a lot of mods installed, could any of them mess things up somehow? Were you able to build Courthouse in any of your other cities?
Your response got me to doing some troubleshooting.
First I tried disabling different mods, starting a quick game to see if that made a difference. No success.
Second, I un-installed Civ 5 and cleared out my local cache in Steam then re-downloading and re-installing. Again, no success.
Third, I tried clearing out all of my mods from the MODS folder and re-downloading from Steam Workshop (%UserProfile%\Documents\My Games\Sid Meier's Civilization 5\MODS). Still no success.
Finally, I deleted the contents of ModUserData (%UserProfile%\Documents\My Games\Sid Meier's Civilization 5\ModUserData) and cache\*.db (%UserProfile%\Documents\My Games\Sid Meier's Civilization 5\ModUserData\cache\*.db). This seemed to have fixed the problem as I could now build courthouses after annexing a city. I noticed that navigating in the Mods menu and loading moded games was noticably faster (slow ,but tolerable).
I'm guessing that there was some corruption in "Civ5ModsDatabase.db". My theory is that because I had Civ 5 since it first came out and experimented with various mods a series of upgrades to the game and the mods broke something.
Thanks for your suggestion.
So now my problem is getting back some of the functionality that I had in the in the older mods: (1) trade screen that showed all tradeable resources and other civs, and (2) economics screen that showed all cities and their contributions (resources, gold, happiness) and current project. I thought this was InfoAddict, but I have that installed and enabled.