My guess is that your generic case came with a fan that isn't equipped with a fan speed sensor, or perhaps even a fan that connects directly to the power supply.
A fan with a speed sensor will have 3 wires and connect to the motherboard like this:
The picture is of a CPU cooler because that was the only good image I could find. However, the case fan connector is exactly the same. If there are only two wires coming out of the fan or your fan plugs into one of the drive connectors from the power supply, there is no speed sensor and the BIOS has no way of knowing the fan works.
Assuming this is the problem, you have a few options:
1) Buy a fan that has a speed sensor (or perhaps reuse the one from the old case)
2) Look for an option to disable fan speed warning in BIOS setup -- although HP BIOS probably won't have that
3) Just ignore the warning