Disk utility's repair disk and repair disk permissions functions, which are run as part of a safe boot, can take quite some time to complete their job. I would

Disk utility's repair disk and repair disk permissions functions, which are run as part of a safe boot, can take quite some time to complete their job. I would just wait. However, if you would really like to know where your boot is getting stuck, do a verbose boot, which is the same thing as a safe boot, except it replaces the gray Apple screen fairly (and usefully) verbosely.