William,
After opening the layer package in ArcMap can you save the layer file to your disk, and open the layer file in ArcGIS Explorer? This is not the solution to the problem, just trying to narrow down the cause... is it the package, or the contents of the package... ??
Also, are you using ArcGIS Explorer on the same computer that you have ArcGIS 10 installed on? This is not a problem, I am just trying to understand the exact setup, so I can ask the right questions, and potentially provide the right solution.
Do you have service pack 1 for ArcGIS 10 installed, or just straight ArcGIS 10?
When you install ArcGIS Explorer 1500, what happens when you try to use it? In regards to system requirements ArcGIS Explorer 1500 is virtually the same as ArcGIS Explorer 1200. There may be another cause for the problems you encounter, un-related to hardware.
Mark