Is the buzzing temperature related?  The engine may be trying to tell you
that it has not warmed up yet.

Most diesel engines have some kind of pre-heating for the cylinders to bring
them up to temperature where the diesel fuel will ignite.  If the outside
temperature is cold, the cylinders need to pre-heat for a minute or so,
depending on how cold it is.  If it's warm outside, the pre-heating can be
almost instantaneous.

It's possible that the buzzer is telling you that pre-heating is still going
on and don't try to start the engine until the buzzing has stopped.

Just a thought, not necessarily the solution.

Clean your battery connections.

Dave