Hi, Some good news.
There are two different flavors of gt440. One is for OEM home theater use and draws 56 watts. The other is for retail: "The GeForce GT 440 for the retail market works internally at 810 MHz, has 512 MB of GDDR5 memory or 1 GB of DDR3 memory running at 1,800 MHz DDR through a 128-bit interface, 96 processors running at 1,620 MHz, and a TDP of 65 W."
http://www.hardwaresecrets.com/news/NVIDIA-Intros-GeForce-GT-440/5364
I assume you will be installing the second, but either version will work in your current PC without upgrading the 250 watt PSU. Just stick the card in and load drivers.
Your processor, e4600, is spec'd with a max TDP of 65 watts, but draws less (the same chip with higher frequency also is listed at 65 watts). Adding the 12V required by your CPU and Gt440 and MB, etc, leads to a total requirement of maybe 120-150 watts of 12V at absolute peak. The 250 watt PSU will handle that no problem.
If you do go with a new pwoer supply, and if you runs games at all, then look at getting a better video card than the gt440. Something like an HD 6670 uses roughly the same power as the GT 440 and is much quicker. Here is a reference for suggested cards
http://www.tomshardware.com/reviews/fastest-graphics-card-radeon-geforce,3085.html -- use the hierarchy chart at the back to compare cards or a something like this: http://www.hwcompare.com/10844/geforce-gt-440-1-5gb-vs-radeon-hd-6670-oem-1gb/
Back to your real question: Open case, read label on your current power supply. Post model number. Post dimensions if given. Look for letters 'atx' on PSU.