Sounds like a corrupted registry entry or config file. This is the nuclear option, but will definitely get it done.
Performing a Clean install of Flash Player on Windows:
Thanks for the response Jeromie.
I have in fact done the steps you suggested. I do agree there is probably a registry problem, I just don't know where to look next!
You might want to Google "Microsoft Fix It". That website provides numerous solutions to Windows problems.
Here is an example of one solution:
Thanks Andy, that sounds really useful.
I'll give that a go when I can next get access to the machine, and i'll report back after.
Andy that seems to have resolved it!
Tried product codes for the last few versions, and also ran ccleaner over it (which i'd done before) and it appears to be working ok now.