Kitten,
I think it is very uncommon for cats not to want to use a litter box. Sometimes not using the litter box is a symptom of something more serious. Have you talked to your vet about your cat issue? Also, I found this link that may help with your cat issue.
http://www.thecatsite.com/t/9563/ina...blems-answered
Oh....and I love those historic buildings with insanely high ceilings!