It's possible that the layer package doesn't actually contain the necessary data. Here's how you can check:
In ArcMap, display the layer properties of the layer in question with the exclaimation point. Click the Source tab and look at the pathname to the data. I suspect it might be referencing a local SDE geodatabase. This layer package will never display properly because it doesn't contain the data. When the person created it, they specified that the data should not be included; there is a checkbox that must be checked when creating the package that says: "Include ArcSDE Geodatabase data". If this is not checked, the layer package won't contain the data.
Thanks,
Mike