I wouldn't recommend it, but then again video card manufacturers have a tendency to put higher energy requirements on video cards to avoid being blamed by people who have a crappy psu's. I highly doubt that a 250 w psu could handle the card, and the potential of frying your components is just not worth the risk. Instead I would recommend buying a high quality psu and replacing the one you have. It's a fairly simple process and you should go to newegg.com to find one that fits your price range and requirements.
We still need more details on that PSU, the most important being the 12V Amp rating.
You could go here: http://extreme.outervision.com/psucalculatorlite.jsp and fill in all your system information, selecting the 8400GS in the video card option. It'll give you a rough estimate as to your power needs.
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