The same thing is happening to me since yesterday. I have a botcamp partition and I can boot from there, but the os x partition right now is off limits for me.
I went to recovery and used disk utility, it said this: "invalid index key. the volume was found corrupt and needs to be repaired". but disk utility can't repair it.
I have an IMac tell based desktop which has started to take ages to do anything, almost as bad as windows. Now the computer comes up with a grey screen and then shuts down on its own.
Before you do anything backup the whole system using Time Machine and if you can create a second backup using a bootable clone. You may have a hardware problem and you need to preserve your data!!!!
Your HD sounds like it's beginning to fail. I would strongly recommend running Apple Hardware Test in Extended Mode. You should run it 2-3 times to ensure AHT picks up any errors, running 1x doesn't always pick up errors. If you have any errors then it's time to take it in for service at your local Apple Store or AASP. If you have AppleCare coverage then call them immediately and tell them what you have done and they will advise what your next step is.