Random reboots during sleep and laptop won't turn on if plugged in.

The issue I’m having with my Air is that it will randomly bong during sleep, and sometimes I’ll open the lid, and it’ll show a white apple and boot up, and other times it shows the login screen with no backlight. It also appears completely dead if it is turned off with the charger plugged in, not responding to the power button until I unplug the charger. I reset the NVRAM and unsuccessfully tried to reset the SMC, but nothing worked. Can somebody help me figure this out?