I had the same problem on Vista 32 bit with 4 gb of RAM a Quad core processor and an nVidia 8800 GTX with 768 MB of DDR3 ram of it's own. I could install and play up to House Party and after that it said I was out of memory

LOL
Erm, I don't think so

Sims one just doesn't get quad core and me thinks it is going to go into meltdown trying to figure out 64 bit. As Hawk said, it just doesn't understand such technology.
Of course if you find a way to prove me wrong I will be more than happy as I have just received my copy of 64 bit Windows 7 today. It would be nice to play the original again