Using the ESXi shell command lspci -v showed the card present in the host, but why wasn't the driver seeing it and loading?
Turns out if the firmware of the card is too old, the newer driver doesn't acknowledge the presence of the card. On a wild guess after poking around the VMware HCL, I uninstalled the 3.2.6 driver and installed version 2.3.9 which was also listed as being compatible with ESXi 5.1.
Eureka! The card was found, but a warning was present to update the firmware.
Updated the firmware and the card was good to go with the old 2.3.9 driver.
Then I updated the driver to 3.2.6, flashed the firmware again with the 3.2.6 compatible version, formatted the card and finally I was up to date with a working card.