I had this happen to me in Jan. 2015 and posted my experience on another thread to which I am copying below. Good Luck!
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I posted the below on another thread this week after I had 5 inactive Disney GCs from Target. Thanks to someone posting the direct phone number to the Gift Card specialists, I was able to get this worked out really quickly!!
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I just received some Disney GCs that I ordered from Target as well and half were inactivated. I saw on the Disney GC Deals thread on this board that someone posted a phone number, which I called today. I was on the phone for about 10 minutes, and the rep. took the GC numbers down, said she would call Disney, and get back to me by the end of the day today. I will update this response once that does (hopefully) happen.
Target Corporate Gift Card Line: (800) 544-3875 - spoke to a real friendly woman, sounded like she was located in the U.S., and knew exactly what the problem was.
Have your Target order number ready, along with the 24 digit gift card number. Mine were located on the back of the card, but the rep. also said it could be printed on the cardboard backing, so keep that too!
ETA1: 10 minutes after I got off my first call, the rep. called me back saying she got all but one activated herself. The last one she needed to take the 16-digit GC number and call Disney to get it worked out. So far, relatively painless to get it resolved (though I wish I just got them all activated originally).
ETA2: Another 20 minutes and all GCs were activated. Again, this was rather painless, and I didn't have to talk to multiple people who didn't understand what I was talking about, or have to go through Target's "normal" customer service.