It looks like a relay. Could be a dirty connection, i would check battery terminal and eye connections. And any other connector that could be dirty/corroded.
Freddy, what was your solution? I stalled my B7610 when the running mower deck high-centered and now it won't start either. Makes the same buzzing sound you described from under the dash cowl. The amber glow plug dash lamp won't illuminate either when attempting to start.