Could you please try this:
Shut down the computer, take out the card, and boot into Windows NT (thereby ensuring one start without the card).
Then shutdown, put the card back in, and boot up. Run the NI-Serial diagnostics - do the ports now show?
If not, can you try to toggle this BIOS setting: "Plug and Play OS installed", and repeat the steps above?
If it still does not work can you specify what kind of computer is it (eg. was it purchased from a manufacturer like Dell or custom-built, what BIOS version)?
Another question: Did you have the card in the computer before installing the NI-Serial software?