Hi kduck,
Different beep counts indicate different parts failure in the computer.
To isolate the issue,please remove all the external peripherals, the power cable from the desktop, press and hold the power button for 20 seconds. This process will drain all the static energy from the computer.
Now connect only the power cable and restart the system.
Please listen to the beep sounds carefully and count the number of beeps and the order in which the system beeps. And also check the status of the 4 LED lights at the back of the computer and reply with the LEDs lights status and beeps sounds if any.
I would check the problem depending on the status of LED lights and help you further.
