Here is something you can try immediately courtesy of our tech support folks:
"Without a crashdump it�??s hard to tell, but I�??m guessing it is crashing because hardware acceleration is on and they have an old, corrupt or otherwise compromised graphics driver or card.
To turn off hardware acceleration, go to Customize->ArcMap Options->Data View tab and uncheck �??Enable Hardware Acceleration�?�. Then try adding the basemap.
Alternatively, they could look into updating their graphics card drivers from the manufacturer�??s website but this is something most novice users don�??t like to do."
Let us know if this resolves your issue.
Christian
