New cat 4yrs old wont use kitty litter and is not eating or drinking much

We have just bought an older cat from a cat shelter. She is 4 years old and we assumed she would know to use the kitty litter. We let her have run of the house for the first day (apparently not the thing to do) and she pooped on the carpet..... then read that we should lock her in a room with enough food and water with her kitty litter and she would work out the rest. She was in there all day yesterday and last night and she still has not pooped!! She also isn't eating much food. It is Tuesday and she last eliminated on sunday morning (a healthy stool as well). She will stay in the room today but I'm worried we are doing something wrong? She also isn't eating or drinking much. We have an indoor plant and she tried to pee on that.... We have tried a couple of different kitty litter now using one that looks much like dirt, but still no luck. Can anyone suggest anything?

How is kitty acting, aside from not eating or using the litter box? Is she playful/affectionate or is she hiding/standoffish towards you?

It is actually quite normal for cats to not eat well and not use the litter box for the first day or two when coming to a new home. There are lots of new smells, sounds and people to get use to.

Do you have any history on this girl? Was she a stray or owner surrender? How long was she at the shelter? Did you interact with her at the shelter? What did the shelter workers say about her disposition/personality?

Also, I recommend investing in some Feliway diffusers. Amazon has the best price that I have found.

Thanks for responding. She is an affectionate cat, loves a pat and is not standoffish at all. She likes to hide under tables so she definitely has a shy side. 

She was owner surrender and had a litter that all sold from the shelter before her. I believe she was only there for less than a year. Yes we interacted with her, she came up to us straight away and let us pat her - she showed signs of affection so that helped make our decision on getting her. The workers said she was an affectionate and quiet/shy cat.

Toady I bought some cat mince for her as that was what it looked like the shelter was feeding the cats. She had a little nibble so hopefully she eats more later. Also, the shelter were using straw in their litters, should I buy some and change the litter box again?

I would recommend getting a second litter box and placing the same material in the box that the shelter was using. In the original box, keep whatever kind of litter is already there. Switching types of litter so frequently can cause problems. If you see that she is using one box over the other you can just keep that box.

Was kitty kept in a cage at the shelter or did she have free roam in a room (or both?)
If she were caged, you may need to confine her to a smaller space (or a large dog crate) to get her acclimated to using the box at your home.

I would try adding rescue remedy to her wet food and some in her water - good luck !