The problem with "old school bit mining" is that depending on your luck, it may:
- not work
- work some of the time
- be unstable
- work as expected
- blow stuff up
Unless HP went full-evil and used a bastard voltage between the PSU and motherboard voltage regulators, the connector probably has 12V, GND, 5VSB, PS_ON and not much else. In that case, it could easily be replaced by an ATX PSU with sufficient rating, just need to create an ATX-to-whatever adapter to run everything from a single adequate size PSU.