Is there any possible way you can upgrade your current power supply?
Even if its not a standard ATX power supply, we might be able to help you if you give us the dimensions, or figure out if its mATX or ATX...etc..
There are other solutions for powersupplies, specifically drive bay power supplies that are specially designed to only power graphics cards.
On the other hand, if you have no other choice, your system could probably handle an ATi 4650, and barely push a 4670, but i think you should realize,
Youre reaching the end of your pc's life span. If it really only has a 250w power supply, I dont see any point in trying to upgrade the pc any further past this point.
OH: It'd be helpful if you could provide us with the maker/model of your powersupply. And your budget (if you have one) Just so we know what we can work with.
Pretty much what ^ said. If you could tell us your budget, we might be able squeeze in a power supply too and still have you get an improvement in video power.