"Disk Utility is indicating that, “This drive has a hardware problem that can’t be repaired. Backup as much data as possible and replace the disk. See an authorized Apple dealer for more information.” It is not letting me repair disk permissions."
WAIT
STOP RIGHT THERE
cmaier has given you THE BEST ADVICE YOU'RE EVER GOING TO GET.
LISTEN TO HIM and follow it.
Download CCC RIGHT NOW (don't even finish reading this post)
Get it here:
www.bombich.com
Once you've downloaded it, continue reading here.
CCC is FREE to download and use for 30 days -- this will cost you nothing.
Now you need an EXTERNAL drive that is large enough to hold everything that's on your internal drive.
Connect the external drive.
It should be formatted to Mac OS extended with journaling enabled, GUID partition format.
Now open CCC and accept all the defaults.
Set your internal drive as the source, and the external as the destination.
Turn CCC loose and let it do its thing.
If CCC asks if you want to clone the recovery partition, YES, do this.
The idea is to get the contents of your failing drive onto a GOOD drive, so they won't be lost.
DON'T WORRY ABOUT PERMISSIONS. They're "small potatoes" at the moment.
Just get the cloning done.
When it IS done, you can now boot and run the MacBook from your cloned backup drive.
Reboot and hold the option key down continuously until the startup manager appears, then select the external with the pointer and hit return.
The cloned backup will look EXACTLY like the internal drive (in the finder).
You need to go to "about this Mac" to verify that you ARE booted from the external.
I'd boot from the external and try Disk Utility again.
Do you get the same results?
LONG-TERM SOLUTION:
Buy a 2.5" SSD, initialize it for Mac, and clone the backup drive (or the internal, if you can still access it) to the SSD.
Then... "swap the drives" -- VERY VERY easy to do on a MacBook Pro.