I`m sorry to hear your new girl seems to be off colour.
I dont know if its any use to you , but I took in an older cat for fostering in January who had been abandonded at the vets as they couldnt/didnt want her any more. Her coat was matted and patchy with scurf galore. She certainly didnt look anything like the British Blue I was expecting to take.
She was very "switched off" emotionally, if you know what I mean. She didnt come out of her pen for about a month, even though I left the door open as much as I could to give her the opportunity. Eventually she did, and so I put the pen away, but she was still very nervous. Thens she began to loose weight, and wouldnt even eat tuna or sardines in the end. I tried everything I could think of to tempt her.
By Easter she was very thin, and I was so concerned I put her back into the pen to monitor her eating and drinking. Suddenly she started eating, and so I suspect she was back into her "comfort zone" again.
After a month, she decided she was fine! Her fur came out in clumps leaving bald bits, but it is thick and shiny now it has grown back. Since then she has been outside in the sun which she loves, and is feeling so much better. I have seen her try to climb my tree, and have shut her in with the chickens on more than one occasion! She uses the cat flap, and will tolerate other cats unless they come too close. She eats anything and everything, and I`ve just put her on a diet as she is looking a bit routund.
I think that at 11 yrs old, being abandoned in the vets for a week then coming to live with my lot, after what I suspect is a long time of neglect, really took its toll on her mentally, and therefore physically. She needed time to chill and get her head around what was going on.
At the mo she is sleeping on the back of the sofa, 2nd favourite place to my knee. She is going to her new home this weekend, and I`m glad she`s been with me this long, as it was just what she needed.
Could you put your newbie on her own over night, so you can see how much she is actually eating and drinking, and to monitor what come out the other end? You could leave a selection of wet and dry food out to see what she prefers to eat. She may just take a while to adjust to her new home.