[oldE]

Nick,

You didn't say whether the buzzing was the sort you hear from an alert buzzer or the kind you hear from a starter solenoid which can't get the starter turning. If it is the latter, try rocking the car in gear to see if you can turn the flywheel past that area.
Failing that, I'm guessing either
a/ a loose connection at the battery. Check both terminals.
b/ loose connection at the starter or bad solenoid. Again check connections, or
c/ bad starter.

Is there a clutch interlock switch on the car? There is probably a mechanical switch somewhere near the pivot of the clutch pedal, hooked into the ignition circuit. If this switch breaks, the car won't start even if the clutch is depressed. You might be able to jump this if you can find it and there is no continuity when activated.

Failing that, call for help.

Les