iMac Will not booting after most recent App Store update

Hello all!

So I've recently updated my iMac ( 21" 2012 I believe) with all of apples most recent updates. I have NOT installed Sierra yet, but I am running El Capitan. So I noticed right before I said to restart to install updates, it bogged down REALLY bad. I had only Pages and Safari running at the time as I was updating my resume. So it restarted and it took a VERY long time to update. I'm talking 2 hours ish. Finally she restarts and I hear the tone. I go to log in and it just spins and spins and spins... won't boot. Thankfully I use TimeMachine and tried to restore from a backup on 9/27 of this year. Restored and now she's bricked... she loads the grey screen and about 3/4 the way through I get an error code (see picture) and it's stuck in a restart loop. I can't lose this computer. I'm somewhat tech savvy, but not very familiar with Linux codes... could someone take a look st the error codes and possibly tell me what it means/how to rectify?? I'm pretty annoyed as this all was a result of updating only Apple apps from the App Store.