Answer: Bad Battery.I bought a new battery, installed it, and the problem disappeared! 
Won't Boot. No Screen Activation. Just fan spinning and keyboard lit up for 7 seconds then off. Tried unplugging battery and holding down power button for 40 seconds  then a reconnecting battery and power multiple times, but no help. Tried no battery and power supply but then the keyboard won't light up. Tried disconnecting hard drive, ram, and wifi card but always the same result; if the battery is plugged in, seven seconds of keyboard lights and fan and then immediately to dead. If the battery isn't plugged in, then nothing. I feel like it's either the battery or the motherboard. Will have to try and replace for the battery first I guess. Any words of advice are welcome.     
Inspiron 7000 2 in 1 Can't start. Keyboard lights up and fan spins for 7 
seconds then off.