I can’t start my computer after installing update

Start from Recovery & re-install the OS.

This will lay a fresh OS over the old one without affecting anything else on the Mac.

I've had this happen several times on different Macs with High Sierra security updates.

Well my attempt at installing the System update worked after all. I started it installing and went to bed. When I got up this morning the update had installed and seems to not cause any problems - yet! I think maybe I was too impatient. But when I tried it I waited for over 30 minutes and the slider had not moved. I don't know how long it took but at least I got it installed. So lesson learned is if your update looks like it won't install, let it run all night and see if that works.