Last night, all my WP7.5 apps stopped working

I have absolutely no idea why. It started (as far as I know) at 2:30am when I woke up with raging heartburn and needed to get downstairs and drink something without waking up the (pregnant and easily woken) girlfriend. I tried to open up the Flashlight app. It showed an opening animation and then... nothing. Back to the main screen.

I managed in the dark.

Today, no apps work at all. Not even Nokia Drive (and this is a Lumia 800 - Drive is one of my favourite apps).

Rebooting the phone makes no difference - apps still behave the same way.

I'd like to avoid a factory reset if possible, if only because reinstalling everything is such a complete pain.

Any suggestions?