Is my hermit crab dying?

i am sorry but that does not sound like a healthy crab ... and not checking out the crab before you bought it was not very smart and also, you do not keep a single hermit crab ... all crabs are harvested from the wild where they travel in large colonies ... a single crab will always be stressed, stress leads to illness, illness to death ... the fact the crab is missing limbs, it could be for several reasons, the number one reason is something off in the environment and considering you just got her, something may have been off at petsmart (highly likely) ... i would return that crab and get at least two healthy ones ... a healthy one will come out immediately when you pick it up ... and please google land hermit crab care and read some hermit crab sites to ensure you have what is necessary to keep these little guys alive ... every crab requires a minimum of 3-4 shells to choose from to change into ...