check engine light fix
 

I am almost positive that its this buzzing problem. There is a buzz coming from the middle connector on the opposite side of the throttle in the engine compartment. The buzzing type of noise changes when you wiggle the wire. Any suggestions on things to try? Last night I was working on my car and had the electric on, the check engine light was on. Then I turned the key off for ~5-10 minutes. And then turned the car on all the way and the buzz stopped and engine light off.

That buzz is most likely normal. Idle control valve makes a buzzing noise for about 12-15 seconds if the key is turned on or off. It is the magnetic control valve vibrating through the field coil which makes the noise. Common thing on BMW unless it is happening without the ignition key being turned on or off

The check engine light is always on when the car is not running and the key is on.

No the CEl is also on when driving car too. And the noise is constant it doesn't go off after 10 seconds.