The cable you are speaking of is a bi-lingual 9pin to 4pin 1394 cable.
No, we do not support connecting the StudioLive Ai mixer to a computer with a 4pin (or 6-pin) connection.
There is no such thing as a 1394a - 4pin FW800 speed chip.
1394 4-pin is a FW400 speed bridge chip. The 4-pin 1394a connector was associated with the Sony i-Link connector which is the non-bus powered version of the more popular 6 pin 1394a standard.
If you have a 4-pin connection on your computer, you very likely have a 1394 chipset which is not supported (most likely a Ricoh or NEC chip). However if you have a computer with a 4-pin connection this most likely means you have laptop. And you may very well have a PC-Express slot. Even if you have a desktop. Please check our 1394a compatibility list for an adapter which we do recommend which will work.
See that article here: http://answers.presonus.com/1672/is-there-a-firewire-compatibility-list-for-firewire-cards?show=1672#q1672