Install it in another PC.
Be sure the drivers for the motherboard chipset are installed for the OS in use.
The second item seems to happen more often than it should. Folk today seem to rely on Microsoft to get the right motherboard driver but that's often broken. The old method of finding and installing is still best.
I recently bought a firewire card for my PC, it says it's compatible with windows 10 (im using windows 10) and that it has Windows built in drivers, and that it supports plug and play. I plugged it in to the PCI express port, plugged the power in and booted up but i can't see it in the device manager - although im not sure under what category it would appear - and my audio interface doesn't register a firewire connection.
How can I debug this problem? Where should the card appear in the device manager menu?

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