I would ask this question in the SolidWorks Simulation/Simulation forum as well.
I take it that you mean that your computers are using the onboard graphics, that neither one has a graphics card that you plug in. If so, that probably means you are skating on pretty thin ice just trying to run SolidWorks, let alone Simulation.
You are also running with very little RAM on your system and not much more on the simulation computer. If your monitor your RAM usage with the Windows Task Manager or Resource Monitor, I suspect you will find that you are using all of your RAM and getting into swap space, which slows down SolidWorks and Simulation. Adding some RAM may help speed up your machine and may stop if from freezing.
RAM is pretty cheap. You could buy some more to get at least 8 GB on the simulation machine and see if it helps. You could also buy an inexpensive SolidWorks approved graphics card, like the FirePro V4900. Personally, I would do both, just to run SolidWorks better, but that may not make sense to you.
can you post a screenshot of exactly what you see in solidworks simulation? also do you see the solidworks process still working or is it 0. (is cpu fluctuating and is memory growing in the task manager)
what version and service pack? commercial or EDU?
where are the files stored?
how many elements is the problem and what kind of bcs are you using? radiation? or just convection and conduction? have you tested those same conditions on a smaller assembly or part?
before you go out and spend money on hardware, i'd at least have someone else try it on their computer.
To go along with Jared's questions. What is the exact make and model of your computer. Desktop or laptop?