Thanks!
I figured it was something like that...it turns out that someone had saved as on an old assembly and it made copies of all those parts with different names in a different folder (they didn't understand how to reference parts to an assembly without being in the same folder).
When someone tried to copy the files onto the new computer, the assembly didn't remember where the parts were located (I thought it was referring to the parts in the correct directory - not the copy directory that someone made). So I was able to find the correct folder and retrieve them 
Although I wish that original person hadn't made completely new copies of the parts for the assembly.