Had a quick look at the max file.
First thing is the scale. Yours would be 32000 meters long in the map.
That's easily fixed.
Second. You don't need to Group the individual parts. You do need to name the actual parts the same as you named the Groups. When you have done this, select all the parts and put them in one Group.
Third. I couldn't tell whether you had applied UV texture coords to the sword. (Don't need to do the dummies). You need to do this to export sucessfully.
Now the tricky part.....
There is a glitch that I have come across frequently with the edges. Sometimes you make what look perfectly good edges and they will crash the max when you try to export. This is what happened when I fixed your sword and tried to export it. Not your fault. It's just a fecky thing that the exporter does. The only thing you can do is to try the edges in a slightly different position/size/shape until it works. Once you get a good export, save the edges to a different file (goodedges.max ?)and then use can merge them into another file. If you delete the edges and export, there is no prob. So you might want to do this just to check the model in the game.
I'll have a longer look later and see if I can get the edges working.
For reference, your parts should look like this before you select all and Group as Blade_Object_CobraSword.