Macbook Air suddenly shut off, now runs slow and sound is broken

Macbook Air

OS X El Capitan v 10.11.6

Processor 1.6 GHz Intel Core i5

Memory 8GB 1600 MHz DDR3

My computer suddenly shut off during normal use while 75%+ charged. When I turned it back on, it was running unusually slow and the sound was not working (speakers and headphones both; pressing volume keys on keyboard shows a crossed-out circle where volume bar should be). Also, the battery now seems to be draining faster than usual.

I tried a hardware reboot, along with entering safe mode and making a new account to see if I could fix the sound. I also tried to reset the SMC by restarting while holding down Shift+Ctrl+Option for 10+ seconds along with the power button, but my computer did not turn on. I turned it on normally. Next step?