The only time I've had a unit that produced a drum solo fairly frequently on power up, it was due to one of two things, both related to a true and complete power down state.
Either the battery had gone completely flat, and I was powering up after connecting to external power, or the unit had been left idle on the desk (or in it!) for over a week without being turned on.
Understand that your TomTom doesn't completely power off when you turn it off with the power button. It's in a very low power 'suspend' mode. Providing the battery doesn't go flat, in about a week's time, the device well and truly shuts off. This is to avoid fully discharging the lithium ion battery pack, something that is very bad for that battery chemistry. Alternately, if the battery goes too flat to keep the unit powered up in this 'suspend' mode while it's sitting (which, depending upon the charge state of the battery and its overall condition, could be anything from 2 minutes to just less than the full week), that will also cause it to completely shut down.
When the device is powered up from a completely off state vs. that suspend state, it comes up as though it had been rebooted, drum solo and all.
Your 720's battery is probably getting pretty tired by now if you haven't swapped it out since you bought it.