OK, so now we've narrowed the issue down to a problem that happens during meshing, correct? Just for the sake of due diligence, make sure that you have "Override" unchecked (and that "Use Elements from Existing Mesh File" is checked) under "Elements" in "Run Settings". Make sure that you mesh (and save the mesh) before running an analysis.
Sylvain made an excellent suggestion, but before going down that route I would try meshing each part independently; i.e. open up each part file and go into Mechanica and try to mesh it. Without being able to see the model, it sounds like there might be an anomaly with the geometry that is creating an issue for the mesher. If you have some very small/oddly shpaed geomtric boundaries in your model (slivers), then the mesher could fail when trying to places nodes and elements based on those boundaries.
Once you've ensured that you can mesh each component in the assembly successfully (and separately), then they next step would be to look at the connections between components. A good starting point would be to suppress all of your connections and set the "Default Interface" in "Model Setup" to "Free" and then try to mesh the model. If that works, then start defining connections one at a time (and meshing after each connection). My suggestion is to start with "bonded" contacts first, then move onto "fastened" connections.
I can take a look at your model myself if you can post a copy of the assembly (and all of the parts) and some sort of documentation outlining how they go together. If you can't (for whatever reason), then follow the above and let us know of the results.
