That header provides two separate USB buses, one for each port on the front. You imply that your new USB2 card has only one internal bus. If you want to hook both ports up, you'll either need a second internal bus (probably yet another card), an internal hub of some nature (probably not the most practical idea), or hook one of the ports up to the new USB2 card and hook the other to the existing header.
Since you need to chop your current cable or create an adapter of some nature anyway, I'd go with the latter.
USB is four connectors, 5V, Ground, Data+, and Data-. Your header presents one port on the odd-numbered pins, and the other on the even-numbered pins, both with an extra ground for some reason.
I don't know the best way to connect what you've got now. In the best world, you could have a new header with wires coming off of it to which you could attach new connectors and plug in the existing connector, but I think you'd be hard-pressed to find such a thing. Alternately, you could pry open the connector you have now to free the existing cable and attach new connectors to the old cable directly. You might even be able to, if you're careful, put one of the existing pairs back in the connector and reattach it to the motherboard.
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Bitt Faulk