Is my new kitty at risk?

I think my 7 year old indoor female has feline leukemia. She has alot of the symptoms. We thought she was just depressed because we had to put our other cat to sleep last Dec for supposed "fatty liver". Now I think maybe he had feline leukemia. Anyway, we got another kitten 3 weeks ago to try and cheer her up but she has not taken to him and is getting worse. She has always been skinny but now she is not eating and will only really drink water out of the bathtub faucet. I can't afford to take her to the vet so I'm just going to have her put to sleep. My new kitty got his FVRCP vaccination at the animal shelter but has not had the feline leukemia vaccination yet. Is he at risk to get sick from the other cat? Help!!