Numpy installation error. (Mingw32CCompiler instance has no attribute 'compile_options')
This is most likely a numpy issue. Unfortunately I could not upgrade theano even after the fix I will suggest, but following a step by step guide like this one might work.
This specific problem occurs because numpy.distutils.misc_util.mingw32() returns False while it shouldn't. See also this discussion and the source. I decided to set manually the system variable MSYSTEM to MINGW32 which was not defined in my system and which I find unlikely to break any other behavior.
As I said this does not guarantee that the upgrade will work nor that there will be no side effects, but it will solve the issue mentioned here.