Ok. I'm a bit confused. According to the specifications of the HP Media Center m7470:
1) It already has a TV Tuner installed.
2) Should have three PCI slots (one available).
The Hauppauge WinTV-HVR-1600 is a PCI card and should install into one of the three PCI slots your computer has.
The PCI slots not the problem. It's the ( I believe) the white 10 or 12-pin connector that it has on the card. The one from HP that came off the old card is shorter with less pins.