a proper burial is in order then...

It looks like you once had a St. Augustine lawn. Without supplemental watering in your climate, you'll end up with what you have in your picture.

Agreed. It really is only mostly dead since it spreads via runners, but it may need some help from additional plugs and the easiest route would be to re-sod that area if the goal is to stay with SA.

I would give it an inch of water and sit back for a week. If you have any shade, no doubt the grass looks considerably better. If when you look at it a week after an inch of water, you don't see any new growth, then you will need new sod.

Where do you live in SoCal? There is every climate and soil type in SoCal, so please be fairly specific.