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Have you tried reproducing this problem with the latest NI-DAQmx drivers (7.5)? Are you able to use the card even though it fails the self test?
It is possible that your system is not supplying the necessary 3.3 V and 5 V supply from the PCI bus. This can be especially true when using industrial PCI or expansion PCI chassis. Verify that your computer's motherboard has a 3.3 V supply for the PCI bus before proceeding with other troubleshooting. Visit Appendix A of the NI 671X/673X User Manual for more information.