Karen L. McLachlan on Feline Inappropriate Elimination (Part 2)

I purchased a 5 month old beautiful all black spayed cat from the local ASPCA 3 months ago. She is my only cat. At first she used the litter box fine but know she has stopped using it completely and sleeps in it instead. Needless to say, she is using my carpet to do her business! I have tried changing her litter and even a different litter box but nothing has worked.
I do not want to send her back to the ASPCA as I love her very much but this can not go on. Please help me!