I am asking if it will work on a 250 w system (Inspiron 531s)...
Well, the 7750, a slightly more powerful and new card, will pull about 250w at max load for the whole system. Most PSU's including cheap OEM ones will not be able to pull their full actual wattage. There's a chance that it would work but if it does, it wouldn't be good. I think your best option would be either a 6450 or a 5670, and still that'll be pushing your PSU harder than it really should.
Will the PowerColor Radeon HD 6750 work on a 250 W system? It is an Inspiron 531s. Is this card worth the money and can my computer handle it?
You need a minimum requirements of 450w psu to run it