windows 7 on a p4 runs alright. you can do basic stuff one at a time. its not until you start running multiple programs at once where it begins to crap out.
if the p4 is socket 478, it will NOT run 64 bit os. if the p4 is lga775 then it WILL RUN 64 bit os.
but looking into that sony model, it has an old 865p chipset. that chipset is from about 2003, and it has a maximum supported memory of 2gb so my guess is that its socket 478, so it might not be compatible with 64bit windows 7.
heres is my suggestion, max out the ram to 2gb, and install windows 7 32 bit.