It actually has separate GPU, PNY something I installed a long loooong time ago, but it has no power connectors at all it's just plugged in to the motherboardSome GPUs will also beep if you forget to plug in their auxiliary power connectors. Though with an HP computer that old, I doubt it even has a separate GPU.
Also, you should open it up and clean all the dust out. Sometimes dust alone is enough to cause these problems. You should see my parents' computer...
Should be fine then, unless it has failed for other reasons. If you have good ears you might be able to tell if there are multiple speakers, and which one is beeping.