@CampfireTales,
Thank you for posting your query on HP Community,
Three beeps that repeat after a pause and occur when you power on your computer indicate a problem with graphics.
In this scenario, I would suggest the next step would be to reseat the memory and graphics card on your PC.

You may refer to this support document for - HP Desktop PCs - Computer Does Not Start and Emits an LED or Beep Code
Let me know how it goes for further assistance.
That said, If the information I've provided was helpful, give us some reinforcement by clicking the Accepted Solution and Kudos buttons, that'll help us and others see that we've got the answers!
Have a great day!
Jeet_Singh
I am an HP Employee