Can you get this drive to work on any other computers with the firewire port? I had a disk that was dual-mode (firewire and USB2) and eventually the firewire port went bad and I had to use it over USB. The soldering of the firewire can easily snap or crack if the unit is dropped or even if the cable takes too much movement or stress while plugged into the unit. If you can get the drive to work over firewire anywhere else, then go deeper into the issue on your PC, but first make sure that the port isn't bad.
TweakUI is, from my understanding, used to make adjustments to the user interface (UI) in windows to make everyday use as quick as possible; I don't see how it would be helpful with this issue.
You've gotten other devices to work on your PC's firewire ports, so the FW card itself or the isn't the issue.
You've gotten this drive to work on the USB port, so the drive being a brick isn't the issue.
You've tried multiple ports with multiple cables, so it isn't a port on your PCI FW card or the cable.
Yes, usually the dual-firewire ports on such a device are for daisy-chaining, but either would normally work to plug into...looks like you have indeed tried both ports on the HD., but the logistics of the drive come into play here, because many times the ports will be attached to the board (on the HD) in one location so that when one goes bad, the other usually comes with it.
The plug-and-play ease of firewire would not lend any believability to the theory that some "port conflict" or something of the sort exists in this situation...I still feel strongly that if you try this HD out on another box, you'll find that it still doesn't work. If it does, I stand corrected, but firewire is a very simple connection protocol, and with all of the steps you've taken (uninstalling and re-installing the PCI cards, rebooting, trying different cables on 2 different PCI cards and on different ports) I have to believe this is something physical on the drive.