Here's a picture of only 2 of the 4 holes! It's crazy!

$3,000.00. Really? For what exactly? I would use a stud finder to locate the studs, move the brackets to the new locations, and then patch the holes in the drywall. Am I missing something?

Trust me, there are studs in the walls. Otherwise your drywall wouldn't be there.

Take the advice of jelly, or you could run a 1x3 or 4 across the studs and drywall. Then fasten your brackets to the 1x right where they are mounted.

Patching the holes is optional. I'd turn em into a piggy bank.

If it's any comfort, the same thing happened to me when my better half stepped on a bottom shelf like this to reach one of the higher ones. I found the annoyance factor to be much greater than the effort involved in fixing it.

I agree that there are studs in your wall, and you don't even need a studfinder: just get a stiff piece of wire and probe sideways through those convenient holes in the wall, then measure the sideways distance so you can transfer the measurement to the front of the wall. Once you find one stud, the next one is likely to be placed 16" away. It looks like the shelf was overloaded -- or stepped on? -- but that's not an excuse for the original installer to not have set the brackets so they could be screwed into the studs.

Based on your original post, I am guessing that you have next to no handyman skills. If you think it is beyond your abilities to fix this as explained above, any friend with pretty minimal skills should be able to remount the shelf correctly in about an hour. Patching is fairly simple, but requires a couple of steps, with time in between for the joint compound to dry. If you want more specific instructions, ask here.

If I lived nearby, I'd fix it for you for $100. Run away from whoever gave you a $3000 quote. I know Hawaii can be expensive, but the person who gave you that quote probably has a second job robbing banks.

And one other thing. If you don't want to patch the holes, follow Roof35's suggestion to attach a 1x4 to the wall. Make sure you know where the studs are so the 1x4 can be securely nailed or screwed to the wall. Once it's mounted, it will cover the holes.

And to add to what everyone else said, except for the time it takes to go to the store to buy a board and when done to paint the wood, all that should take about an hour for a tyro, or fifteen minutes for someone practiced in such things.

Remember with a board that the braces will mount lower on the wall a bit.

A couple of other points. The shelf is bent. It will need to be straightened or replaced.

Using a board on the face of the wall would require that the shelf be mounted further out on the wall or it will slope towards the rear wall.

$3000 to repair that? please post a picture of the quote with the contractor's name and address so we can harass him.

"Using a board on the face of the wall would require that the shelf be mounted further out on the wall or it will slope towards the rear wall."

No. The angle of the braces is not fixed and they would be slightly more vertical screwing in slightly lower on the wood than on the original wallboard.

if you used wood to cover the holes and mounted the braces at the same height on the wall my comment is true. If you used a wide enough board and could lower the position then yes it could be made level.