start button energise a relay that latches open and provdes the current path for the very heavy draw of heaters, and motor.
the relay is dead, or dying and instead of locking open is fluttering like a doorbell (buzz buzz).
Not a repairable item, it is replaceable and not very expensive, much less than a new dryer, last one purchased was $29.99
Relays are common to many dryers, the local parts guy will have one to match if you take the dead one.
typical relay looks something like this, not all are transparent
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