If it ain't one thing....

HOW DOES the "buzz" work?

When you have a problem, and turn the key to start, that causes the starter relay to be energized and pull in, and that sends power to the starter solenoid, which draws a lot more power. If there is enough power to pull in the starter solenoid, then the STARTER starts to try and pull a lot of power

So depending on how bad the problem is, at some point "the problem" causes the voltage to fall very low, and low enough that the start relay cannot stay engaged. So the start relay opens, the starter solenoid drops out, and because there is now no load on "the problem" the voltage at the key goes back up and you start all over again.