Can not update my system and not able to repair disk

I havn't used my macbook pro for about a year, and recently I need to travel to another place and need it with me.

I see in AppStore that there is an update for my ios, I downloaded it, and run the install.

however, when updating my system. I run into some error, the installer says the update installation failed, and I should restart the computer and repair the disk before continue.

I tried to restart in safeboot, not working, the screen stucks at the apple logo for over half an hour.

And tried to restart with my harddrive, the system tells me I can not select that disk to restart.

I an able to run disk utility from the installer. I can verify disk permissions .

But when I run the disk verify, it gives me an error:

Verifying volume "Macintosh HD"

Checking file system

Performing live verification

Checking Journaled HFS Plus volume.

Checking extents overflow file.

Checking catalog file.

The volume Machitosh HD could not be verified completely.

Error: This disk needs to be repaired. Click repair Disk.

But the "Repair Disk" button (and the repair permission button)is gray and can not be pressed, when put my mouse over the "repair disk" button, a line of text shows up:

"repair the structure of the disk's file system, if necessary

Not available becaue the selected disk can't be written to."

the repair permission gives me "Not available becaue the selected disk can't be written to." as well.

What do I do now?