Well, I'm quite amazed not a single person has replied (funny how my
other problem has gone unanswered too). Guess I must have very uncommon problems!
I'm glad to say I've managed to fix it though. As described on a website somewhere, someone else managed to fix it by restoring the registry keys associated with it.
I decided to export the ones on my mum's laptop, delete mine, and then import her's to mine. It seems to be working fine! All Power Options are back, I can change how my PC shuts down, and I can Sleep now! And this was all without a restart. I'm guessing I can Hibernate also; I'll find out when I want to turn my PC off later.
If anyone else has this problem and needs a copy of the registry keys, I can send you them (I believe they work regardless of the computer. I had concerns because it was a laptop, but it seems fine). I'd rather not post them publicly as I am not sure of the sensitivity of them.