The freezing up is *definitely* a heat issue. When we set it up with a fan on high to provide airflow for cooling, it worked just fine for a couple of hours, which leads me to believe that the cooling fan is broken. If I've got this right, the cooling fan and the mother board are a single unit in the Thinkpads (and most laptops), so the motherboard would have to be replaced?
The good news is once it was running with the fan blowing on it, I was able to back up all of my data, pictures, email files, logs, etc. - a big relief.