A few seconds after the PiP is turned on and I start moving, it gives a little beep. It's not the doors locking because that happens a few seconds later when I speed up.
Might be what's left of the seat belt beep. I minimized the reverse and seatbelt alarms, but I still get one for each.
Oh, one other thing I recall somebody discovering once - it was their cell phone, announcing that it had connected via bluetooth to the car.
It always happens a couple of seconds after I start in motion, the first time after power on. When it beeps, a white rectangle shows in the bottom right of the Advanced Nav display for just a second and then it goes back to the Screen Off display. It's not the connection to my phone; that's already come up (silently).
Solved. It's the caution message at the end of the nav system startup. When the (Advanced) nav system starts up, it displays a caution message to drive safely and not to trust the maps. After a few seconds the message disappears and the Continue button at the lower right flashes white for a second. And it beeps. Just after powering on, I usually shift into reverse to back out of my garage or the parking spot. This turns on the backup camera, which suspends the nav system startup process. Then I shift into forward and start off. Three or four seconds later the nav system gets to the caution message, displays it for a few seconds, and beeps to get my attention just as the message disappears. Probably not the most useful place to put the beep. Perhaps the lawyers told the programmers to put it at the beginning of the message and the programmers said "We'll show them who's in charge!"
I think what really happened is that the lawyers required the warning message. Toyota/engineers got customer feedback that the message was annoying and added an automatic press of the Continue button after a few seconds. The beep is the audible confirmation of a touchscreen button press just as you would hear when pressing any touchscreen button. It just so happens this particular button press is automatic.
I have a 2010 Prius, no screen or nav. I just started hearing this same ding/beep that you describe. I will go in reverse and then drive, and a few seconds after I start driving forward, I hear a ding. It's more musical then the standard beeps. It can't be the nav system in my car because I don't have that. Any more ideas? Thanks.