The "span" mode on a switch is intended to let you connect a standard cable from that port to a normal port on another switch by switching the transmit and receive lines (i.e. so data transmitted by one switch hits the receive lines on the other). This is generally equivalent to using a cross-over cable to connect two normal ports on two switches. It doesn't have anything to do with enabling promiscuous mode on a network card
The ports on network interface cards do not expect the transmit/receive wires to be crossed this way, so when the switch tries to send data to your computer, it is arriving on the transmit lines rather than the receive lines and vice versa.
There are some network cards that would work with the setup you've described, but they would just be detecting the cross over and correcting for it, rather than providing any more features over a standard card.