Thanks for your quick reply. Installing a fresh copy seemed to work. I had done all the other steps you listed before, but with an older download, so I think it was installing the new copy that worked.
Now FSX is just really, really unstable, and crashing repeatedly after just a second or so of loading. Event viewer shows:
Faulting application name: fsx.exe, version: 10.0.61472.0, time stamp: 0x475e17d3
Faulting module name: unknown, version: 0.0.0.0, time stamp: 0x00000000
Exception code: 0xc0000005
Fault offset: 0xffba01b7
Faulting process id: 0x1324
Faulting application start time: 0x01d1cb0f1a526b20
Faulting application path: C:\Program Files (x86)\Microsoft Games\Microsoft Flight Simulator X\fsx.exe
Faulting module path: unknown
Report Id: 93eb3b60-3702-11e6-9658-00044b17a245
Unless you have any ideas, I think I'll just have to uninstall and reinstall FSX with all the addons.
It's not the first time this sort of thing has happened.