I had the same issue with my starfish. I agree that acclimation is part of the problem, but all the responses seem to be telling you what you did wrong instead of any possible solutions. Further, if you just added the star, the starvation would not be your fault being that it was being housed at the lfs. Thus, you never had the chance to feed it feed it before it started to melt. Now to some potential solutions...
First, yes, the starfish is starting to "melt." The fact that the melting is starting in its central disc means that it is in big trouble. Again, I had the same issue with the same star, however, my star dropped two legs in the process. That being said, food is key at this point. I would try to spot feed the star some shrimp ASAP. I would literally just take a baster and squirt some shrimp on top of it. I would also add a little phytofeast into the tank to give the star another potential food source.
Long story short, after spot feeding my star for two weeks, keeping the inverts away when I could, and ensuring that my parameters were consistent, the star regenerated both legs and is alive and well. This kind of success is rare, but at least it will give you a fighting chance...