Do you know how to get into CAT mode to check the programming? It is possible it is just one card as the numbers are not necessarily consecutive in the system (any extension number can be assigned to any port). If you can get into CAT mode use command F52 de extn No de and that will return the len number of the port. If these are all around the same number the odds are it is a card. How many are faulty, there are 8 ports (just a note the numbering starts with 0 - 7 for the first card) to a card so if 8 are faulty, that would also point to it being one card.
Another question is are they digital extensions or analogue. If they are analogues, are they all the analogues on the system. If they are it could be a problem with the register, Does your system have an RSTB card (or something like that). Do you occasionally get dialtone no the problem extensions as it may be that just some of the register channels are down.
I am asking a lot of questions but I'm hoping to speed up your resolution by doing so.