Yes, you'd need to let go of the button sooner. Holding it that long takes you to the black and white diagnostic page.
That said, when the device does reboot and the logo comes up, there should be sound with that no matter what state things are in firmware wise. So I'm back to post #2.
If it's just the speaker, that's easily tested (by someone who can disassemble and has a little skill) by applying 1-1/2V battery across speaker terminals to see if it does anything. Should pop and scratch a lot as contact is made with the battery voltage. If not, speaker is dead. Next trick is finding one of correct approximate size to replace. However, if speaker makes noise, the problem is either connection to board by speaker wire (fixable) or driver on board for speaker. The latter isn't something that is going to be fixable.