The description says it all.
I have used GOG's repair function and have reinstalled it too.
There was no apparent visual bug when I left the game last time, just tried to reload a previous save and it didn't let me.
When I start a new game, I select one of the three character, it plays their little animation and it just stands there on that screen. Does not react to loading ANY save file.
Shit, fuck.

Even though there was no apparent visual bug it seems that a memory overflow might have occured in your game. Usually this is accompanied by red squares appearing in the UI, but not necessarily. If this is the case, all your saves made while in this state are corrupted and you cannot load them. But saves made before this state occured should still be all right - but there is an important thing to know: If you try to load a corrupted save (without success) the whole loading mechanism glitches and you cannot load even an uncorrupted save until you quit the game and launch it again. It seems that the same may be true for when you try to start a new game after trying to load a corrupted save. The solution is simple - find the most recent, uncorrupted save and continue from there.

There is no known solution how to prevent the red squares / memory overflow issue and some computers seem to be more prone to it than others (meaning, most players never encounter this problem, fortunately).