At power-on, your mac starts the fans, lights up the screen, and chimes. That means it has passed the Power On Self Test. Next, it gets a Blob of software (containing the dark gray Apple) off the boot drive using a very primitive method (the file system is not loaded yet). Then it does a lot of initialization, and eventually initializes the file system. Next it tries to get the File System to Mount the Boot Drive so it can continue loading.
If the drive can not be mounted, you get a progress bar and spend five minutes doing a disk repair. When completed:
--if the drive can be mounted, loading continues.
--if the drive cannot be mounted due to too much Directory damage, your Mac will shut down, since it cannot proceed.
You will need to use Recovery mode to run Disk Utility and run repair disk repeatedly until it comes clean or gets stuck. If it is stuck, Your drive cannot be written to.
Buy a new Drive and an external enclosure and Install mac OS X anew on it. Then use that Mac OS X to rescue anything still needed from the old rive, with Utilities like Data Rescue. Once you are satisfied, you can swap drives around to get the new drive where you want it.