AFAIK, The 250 = rebranded 9800GT = rebranded 8800GT.Can't find any spec about the motherboard used in this PC but it is a very very safe bet that it will have the port to run an 880GT in (port is called PCI-E). I have seen Crysis ran on an 8800GT before but i'd say if you can afford it jump up to the 9 series and get a 9800gt or 9800gtx or the 9800gtx which i think has been rebranded as a GTX250. Depending on which of the specs you've listed is correct for the system you might look at upgrading the CPU as well, the Q6600 or the E7400 are normally very highly recommended. Let me know if you've got a set budget for these upgrades and what your monitors native resolution is.
PS Welcome to CF
I know that's how it was to begin with - it might have changed now though.