Since you're unsure of your kitty's age, you might want to take her to the vet to make sure she's OK. She could be in the early stages of renal disease (very common in cats, and absolutely treatable through diet), or she might have any of a number of physical issues that would explain her behavior. Once the underlying problem is solved, the behavior will be solved too.
I agree with the others who have mentioned a UTI. Please don't think that a UTI is a minor thing. In some cases, by the time you see the symptoms, the cat's life can be in danger.
Another possible problem is a chronic form of cystitis. If that is the culprit, the vet can prescribe medication to keep it under control.
I've heard great things about a litter called Cat Attract. It's scented to lure cats back to the litter box so they will begin using the box appropriately again. I'm pretty sure you can buy it at Complete Petmart and other pet supply stores. If you can't find it, just Google the product name and look for a retailer in your area.
Has anything in your cat's life changed recently? If this is an emotional issue, a little bit of Bach's Rescue Remedy (a naturopathic remedy that works for people too) can work wonders in helping her to deal with stress. Again, a Google search of "Bach's Rescue Remedy + cats" should give you a good indication of dosing for cats. Another good one is Calms Forte tablets, which can be crushed up and put in a treat, like braunschweiger (which kitties love!)
Make sure the litter box is a good distance away from her food dishes. The old saying, "Don't eat whee you...ahem...poop" is true. Cats don't want their food or water source to be near the box.
I'm obviously a cat lover, and I hope you'll be able to find a simple solution to the problem soon. There are too many homeless cats out there, and yours is so lucky to have a good, loving forever home!