i would go to the vet ASAP. but first i would try feeding it tuna juice. if she doesnt drink it force it with like a cough med. syringe.
my cat that i got in march was named tristan. we got him on a wed. & had to put him to sleep on the following tues. he wouldnt drink or eat so we forced him to drink tuna juice. he had a diese that there is no test or cure for. ther vet that declawed & nuetered him said take him back to the humane society you havent attached to him yet, you've only had him for a day. on the tues. we put him to sleep, i woke up at 5 am, a school day, and he wasnt moveing so i woke up my mom and she stayed with me. i loved that cat so much. it was hard to let him go....now i have a b&w cat named cookie, shes so sweet!!!
you do need to take kitty to a Vet and asap, she needs blood work done,...not eating is a huge issue it only takes 24 hrs without food for their systems to begin with major problems....if you cannot get there today, I would liquefy some of her can food and give her at least a small amount every few hours by dropper....she needs to have some nutrients and fluids asap.
With a 13 yo kitty there could be many issues going on for her not eating, yes it could be her teeth, it could be she needs a change in diet(be very sure its canned)....or it could be something more serious, please don't hesitate to help her.
and please post again and let us know how she is doing....welcome to our cat forum, I hope we can be of some help to you...but we can only suggest here it has to be a Vet to do a proper check up and diagnosis.
the diet the cat is on might lack fiber or protein,or the cat might be allergic to something in the food,maybe try clicking on the top of the page and click on pets then ask a vet to get an opinion of a vet,but you should take the cat to the vet because it could be a serious condition.
My cat actually just ate half a can of her food! I am still worried about her, she is very thin and getting older. I took her to the vet about a month ago where they did blood work and they said all her organs and such were working just fine and it was still just her thyroid. The vet told me to double her medicine so I have been doing that but she still isn't gaining weight. Thanks everyone for the advice!