Let's discuss why this is such a very very bad idea.
First of all, the protocols used by USB and IEEE-1394 (Firewire) are completely different. So when the Firewire port sends its 1s and 0s across to the USB port, the USB port won't know what to do with the 1s and 0s since they are in the wrong format. It's kind of like someone speaking English to someone who only knows Russian. It won't make any sense.
Secondly the speeds between 1394 and USB are different, so the devices won't even recognize the 1s and 0s.
Finally, the voltage levels used can be different. Luckily the 1394 side is only a 4-pin connector. If it had been a 6-pin 1394 connector there would be a chance that this cable would damage equipment, as well as not working.
The advice to find a card is correct. Some active device/card must translate 1394 data into something your computer can understand. BTW, HDMI would be even more difficult since HDMI transmits uncompressed video and 1394 uses MPEG2 compressed video. Also it is very rare to find an HDMI input port, which is what you would need.
You could see if you can borrow a computer that has a 1394 port. Many laptops from the mid-2000s had them. Save the files and send to your new computer.