Hey,

I've been kicking rocks for the most of the year, this S10 died off with my wife in the driveway (thankful as I am to not have to have pushed it back to this point) and when I got in, turned the key to On, there was buzzing noises that would alternate in location.

Troubleshooting, I found that turning my headlight switch stopped the noises, at first. I changed this and now I have three relays that had buzzed.

The Turn Signal/Hazard light relay located behind the glove box - Removed
The HDLP Relay in the fuse box under the hood - Removed
And there is a...junction box? Under the drive side dash, right above the e-brake lever, lots of wires and pins, that buzzes. I'm stumped for this one, I loosened the mounting bolt at the center of it and removed it, and I'm staring at a lot of pins, but I got nothing on what the issue could be.

The battery is shot, and I use an external power source to provide current to the system.

EDIT: Digging around some, that box is a relay box (where the relays are located on top of it).

 

I know an external source could be expected to work instead of a battery but I'd want to try a fully charged fresh battery to be sure as what you describe sounds to me like an under-voltage or under-current situation. I.e. the power source cannot supply enough current when the switches are turned on. Or, could there be a short but through something resistive that is large enough to pull-down the voltage supply or draw so much current that the other components do not have enough voltage or current to work properly and instead giving you that buzzing?