First step is to go into the windows device manager and make sure that the ports for the Mimaki are showing up in there - you should see two: Printer Port and Status Port. If windows is not seeing the Ports then there is no way Onyx will.
If the ports are not seen then go to the Add/Remove programs item in the control panel and remove the Mimaki drivers. Reinstall them and then try connecting the printer again.
If this doesn't work then try testing your firewire cable and PCs firewire with another device (vintage iPod, Firewire HD or CD burner, etc). If this checks out OK then you may have damaged one if the chips on the Card in the printer - this can definitely happen if the printer gets a power spike thru the firewire cable. If the card is damaged I'm not sure who currently is the beat at repairing these.
BTW, is the error 11 showing in Onyx or on the printer LCD?