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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)