Welcome to Tom's Hardware Forums,
The Corsair PSU should work in the HP no problem. Are you sure you had everything plugged in correctly? You had the 24Pin and the 8pin ATX (not 8 pin or 6+2 pin PCIe) connector connected to the motherboard?
That is behavior I would expect to see if a PCIe connector was plugged into the motherboard.
If you are absolutely sure you had all connectors right (I suggest double checking), you should begin the RMA process with Corsair. As I said, there is no reason the Corsair shouldn't work (outside of malfunction or being connected wrong)
Good luck