Nor does it seem to be a question of running as administrator, as I have no problem starting and playing the game.
If the game is making a change in the registry or in a "protected" part of Windows when it saves, then running as administrator is worth a try. I've had several games play fine -- until I tried to save -- then nothing, and I lost all my progress. The solution was to Run as an Administrator.
But that doesn't seem to be your problem.
Are you able to start a New Game and save?
Is it possible the game just doesn't allow saving at the point where you're trying to save? Or have you tried saving a bit further along?
Have you tried checking to make sure your save slots haven't mysteriously been changed to "read only?"