The beeps are a code. Make a note of them. Then look them up by googling "HP beep codes" and it should help you narrow down the issue.
RAM is one to check, remove and reseat the RAM after making sure the contacts are clean.
Can you record the beep and link us to the recording, wherever you upload it? It might be a firmware-related beep code, but typically those do not occur 2 - 5 times per hour; they're very consistent and persistent (beep sequence every couple of seconds).