I've downloaded the file and taken a look at the issue. The reason why you couldn't export is because you had the materials set in the wrong place. I've taken several screenshots to walk you through what I've done step by step.
Step 1: Investigation in "Scene" In the Scene menu I have checked the existence of the various materials and they are just OK. See red boxes for both indication I'm in Scene menu and the Materials highlighted.
Step 2: Investigate the assigning of the materials In this step I check if the mesh has the correct material set. Note, a Mesh can only have 1 material assigned. (Materials can be combined through another material but I'm not bothering with that right now). Select the mesh and navigate to the material menu (see red boxes)
Step 2b: Isolate and fix The "materials" selected in the upper red box are causing the problem. In my experience that area doesn't have any real functional use (I never enter anything here). The lower red box however IS of great importance because this is where the material is selected that should be used for the mesh I have selected previously. Note that the selected material in that box was set correctly. By completing this step, your model is already fixed and ready for exporting. However since you had 3 materials each for a specific part of the mesh, I assume that just only one material doesn't cover the remaining parts. See step 3 for the continuation.
Step 3: Completing the model In order to have all the parts of the unit properly textured we've need to either a) recreate the textures so they become one. b) Expand the number of meshes and assign the individual materials (I've chosen for this route in this case) I've isolated the head and backpack and separated them so each part is now its own unique mesh. Once again I go into the material menu and assign the 2 remaining materials for each mesh. --> Completed!
FINAL Note: Because I didn't have the actual image files of the different textures I had to assume that the textures are correctly wrapped onto the model.