I'd pay attention to the noises as the device boots. If something is failing a hardware test then it could hold up the whole boot process. Although normally when there is a hardware problem the printer will display an error message to let techs know where to look and what self start test failed.
If you do not have access to a workign control panel then performing tests is going to be difficult to confirm anything else. You might want to try removing it from the network or any connected computers incase someone it trying to send junk to it while booting.
Your best bet is to continue working with HP and get the printer replaced as a DOA (dead on arrival). The initial warranty on the printer should be more than plenty to get you a new one quickly.