You could use velcro, double-sided tape or an adhesive.
I think that you would be more pleased with the looks and the performance (anti-vibration and "solidness") if you drilled holes and used some nuts and bolts. A set that as small as 6/32" would be sufficient.
Personally I like the look of allen-heads, and they are available in SST, Chrome, and Black as well as other finishes... something to fit every opinion.
If you do drill holes, I would drill the holes in the material that was more difficult to work with (in this situation the metal of the case) and then drill the holes in the plastic by using the already drilled holes in the case as the template. This will ensure proper fitment.
You could also use rivets (for the window), but one must use care as the pressure of the riveter can (and has in my experience) crack the plastic. Some rivet guns do have a pressure adjustment so that this can be avoided.... but not mine.