Buzzing noise from where, trunk? Engine? Maybe record it and post.

 

@keffles ,

It does sound like the starter, but check your battery voltage as well. If your battery is failing, the starter could be stalling for a few seconds, trying to figure out if there is enough voltage to start the engine.

In my 2006 Avalon XLS, I had similar symptoms. The dealer replaced the starter, and the problem was resolved. I successfully appealed that the starter should not have failed so soon, at the time, and Toyota agreed to pick up the labour cost, if I paid the for part. I was happy with that outcome.

Good luck. Let us know what they find. Have a great day.

Regards,
Phil