Layer files don't contain any data, so they often can't be drawn in arcmap, unless you have access to the source data the lyr references. So if you work at the same organization as someone sharing the lyr file and the source of the lyr is a geodatabase that you can see, the layer will draw. However, if you don't have access to the source, it will appear as a broken layer.
If the source data of the lyr file is a map service, then it should display fine. Since you are trying to display world imagery, am I correct in assuming that you want to find basemap layers? Here's a link to the basemap layers that Esri provides.
That is exactly what is not working... the layers from the ESRI map service. The imagery layer from the link provided is the sample I sent in my post above. It worked fine last week, and now shows the layers as broken???
This layer is working for me... I'm not sure why you can't see it. Is there a network issue at your site? If not, I'd suggest calling Esri Technical Support.