There's a stray cat that is dying to stay inside my house,what should I do?

Take the cat to a vet, as others have suggested use google to find one that might do it for free,

But because you have two other cats, its really NOT a good idea to introduce this one at all, it may sound cruel, but it will be better for your own two cats, regardless of how sweet the new cat is. Cats dont share well, and the introdcution of a new cat is a long and complicated process, plus there may be someone out there with a lost cat desperate to find where it got to.

Since prices vary from state to state and every vet charges differently its hard to say what it would cost exactly for a vet visit. And price also depends on what u want to get done like vaccinations and such. I would go to Google.com and search low cost vet clinics in your area and call each to compare prices. When u call the vet offices be sure to ask what the visit will cost, if your wanting to get her vaccinated then u will need to ask what each vaccination will cost. I highly recommend getting her a dose of dewormer from the vet and buying some de-flea treatment like Advantage ii (2) for cats because worms and fleas can spread from cat to cat that could lead to a flea infestation in your home. When pricing vet clinics u should ask how much a dose of liquid dewormer for cats would cost and ask if they carry one dose de-flea medicine, if they do ask for price. If u can afford to I would get her all the vaccinations that she needs too. Hope this helps :)

She could still be damaged and could be dangerous to your other cats. Or not. Just be careful. Go to the vet and ask how much would one check up be costing you. That's the only way to know for sure.