She should have two litter boxes. Some cats like to poop in one and pee in
the other.
Gail

First - vet check. Sudden changes in behavior, especially litterbox habits
(or lack thereof) are often a sign that the cat isn't feeling well. For
example, a cat with a urinary infection begins to associate the box with
pain, so starts going potty elsewhere. Your kitty might have a condition that
makes her hurt when she defecates, so she's avoiding the box. Anything from
IBD to worms can cause pain when defecating, so the vet needs to check the
cat out. Bring a stool sample with you. I've not really heard of a URI
causing defecation problems (it's usually urination), but it's certainly
possible.

After a clean bill of health...Put a second box somewhere besides the living
room, if you really don't want one there. Some cats prefer to use one box for
#1 and one for #2. You may have to start with the box there, then move it
when she's using it consistently. Don't just up and take it to another room,
though. Move it a few feet at a time until it's where you want it, over the
course of a week or so.

It may even simply be that she doesn't like something about the location of
her current box. Has the carpet changed there, too? Perhaps she feels unsafe,
so chooses to go to the bathroom in a location where she feels safer (more or
less open, whatever).

I bet it is the "new" carpet smell. Can you get it steam cleaned? It might
get that chemical smell out of it.