If you have a sago palm that looks like this, don't panic. The first thing to do is to check the caudex (the pineapple, the trunk) and squeeze it to see if it's firm. It is, you'll be OK. If it's mushy, sorry, it's too late and it has rotted. Throw it away.
To rescue a plant like this, take it out of the pot, or out of the ground. Yeah, I know it looks extreme, but you will need to do some serious surgery on this. Now cut off all of the leaves. Yes, all of them. What you will end up with will look like a large bulb with a bunch of roots at the bottom. Knock the dirt off of the roots and set the plant in the shade for a couple of days.
Now, go prepare its new home. If you're gonna plant it in the ground, be sure that it's on a slight hill. If it's at the bottom of a hill, where water accumulates, it will die. Don't do that. Sago palms, like all cycads, hate having their *feet wet*. They like water, but the water needs to drain away quickly. Plant it as if it were a cactus, using cactus mix potting soil. If you're gonna plant it in a pot, do the same thing, but also be sure that the pot has a lot of rocks at the bottom, and that it drains freely. It's being too wet for too long that makes sago palms do this.
In Los Angeles, cycads do very well. Plant them in full sun, on a little bit of a hill. For a plant like this, if the weather is warm, it can begin to leaf out almost immediately. If it doesn't right away, don't worry, just wait until the next season. Cycads only grow about once a year, in quick spurts called "flushes".
Once it's replanted, leave it alone. If you keep watering it, the roots will rot, and it will die. You should water it in well right after you plant it, but resist the temptation to "kill it with kindness".
It's late in the season, but it's been pretty warm lately in LA, so it might start leafing out right away. If it doesn't, nothing will happen until next summer. Try not to look at it.