You put the FireWire port in the Mac? What form is the port? Is it a card that you install onto the motherboard?
Assuming that, your problem could be with Windows 7 64-bit, which does not always install the correct FireWire driver. Bill Hunt's tips & tricks discuss the solution.
Beyond that, you can test the connection by seeing if you can capture video with Windows MovieMaker.
And, if for some reason you can't get Premiere Elements to capture, you can always use a program like WinDV. Video captured over FireWire with WinDV is compatible with Premiere Elements.
Device identification should be automatic, whether Firewire or USB - sadly though sometime it isn't.
One of my Sony devices (A100 DSLR) requires that the camera be switched before inserting the(for the A100) a USB cable or it is not recognised in the Organiser. It you have only been switching the camera on after connecting the cable you might try turning it on before.
From the specification your camera has both USB and Firewire connections. Have you tried the USB?
If the above doesn't work for you then you should probably install the Sony Picture Motion Browser (PMB) software. It may install a driver for your camera.
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