This was reported by deanej over in the Final Frontier Plus bug thread. I have verified that there is indeed a bug in the meltdown related stuff (and still a bug in the general nuke effects). A fix will be posted over there later tonight.
There is no easy in-game fix for an existing game at this point - if you have a save from before it happened (like an autosave) then you should be able to continue from there after a fix is made to the Python and XML.
What has happened in your game is that due to the meltdown some random selection of buildings may have been destroyed by the DLL for the "city" (as far as the DLL is concerned it is a city, not a star system) across the entire system (not just on one planet, since the DLL knows nothing about planets) which is not reflected in the planet data (stored in Python), and buildings of the type that had the meltdown were also destroyed in the DLL but not necessarily in the Python planet data. Ont he Python side, only the buildings on one planet int he system are destroyed (with luck this can make the data match, but evidently not in this case). Having a mismatch between what buildings the DLL things there are and what the Python thinks there are is what causes the "can't build any buildings" problem.
Currently, this issue can be avoided only by luck: if no building has ever been built in the system except on the one planet that starts with free buildings then it would not happen (since that planet would be the one wiped out, which removes the buildings on the planet from both the Python and DLL's data), otherwise it is would require pure luck that no building of a type built anywhere else in the system but not on that first planet is wiped out by the random chance used by the DLL.
The fix will stop the DLL from destroying any buildings itself when this happens - it will all be done in the Python code, which can deal with the planets and won't have this problem.