Yes, an ATX will switch off after 4 or 5 seconds of holding the button down, unless the Bios tells it otherwise (as your bios appears to be kaputski I guess the PSU just doesn't get the message). The motherboard speaker is just a mini-piezo device, so you'd know if it was working ;-)
PLEASE save yourself! Packard Bells really are the {bleep}roach of the computer world! If another motherboard fits then fair enough, but the cases really are worse than the cheapest Taiwanese made recycled Fiat case (as you'll find out if you have it apart a couple of times).
EDIT: ok, on any other ATX motherboard than a PB the speaker will be a piezo device mounted on the board itself. Your PB may well have an old AT type speaker, which would be a small regular cone speaker mounted to the inside of the case, and uses a jumper type plug on the motherboard.
If you don't get any bios info on the monitor then resetting the Bios flash area won't make a difference, I'm afraid.
The bleep above was me describing a certain kind of insect that can survive nuclear explosions ;-)