Hi @alexandwirtz
The singularity error is trying to indicate that there is a part that is not connected to the rest of the model, so the loads cannot conduct into or out of the part.
The following is just a guess. Maybe the pre-check is based on the CAD model, so it is able to detect when two parts are in contact even if the contacting area is small. But the analysis is based on the mesh. If the mesh size is large compared to the size of the contact surface, there may not be any nodes in contact between the parts, like this sketch. This would cause the analysis to miss that the parts are in contact.

If this is the problem, increasing the "Maximum Activation Distance" for the contact pair should fix the problem. This will connect the nodes on part 1 within X mm to the faces of the elements on part 2. Since the problem started when you added the last part, the contact pairs involved with that part need to be edited.
The other possibility is that a distorted element is causing the problem. (The solver only knows that it cannot solve the matrix of equations. It does not know why the matrix cannot be solved.). If you do not see any problems with the contact between the parts, try a finer mesh on the model.
John Holtz, P.E. Global Product Support
Autodesk, Inc. If not provided, indicate the version of Inventor Nastran you are using.If the issue is related to a model, attach the model! See What files to provide when the model is needed.