Looking at the book again, I may have been wrong. Did you try rendering the particles seperately using hardware rendering? or did you just try rendering everything together?
Additionally, I have learned that it was possible to hardware render with less then ideal cards in maya7, but in the more recent versions, it has gotten a lot less plausable.
You can try rendering just the particles by hiding everything else, selecting Hardware render in your render settings and "use geometry mask" to on, then comp them together. If it doesn't work, then I'm afraid I can't help further.