Installing (and using) numpy without access to a compiler or binaries
a compiler is unavailable, and no pre-built binaries can be installed

This... makes numpy impossible.  If you cannot install numpy binaries, and you cannot compile numpy source code, then you are left with no options.
Assuming performance is not an issue, is there a way to deploy numpy in a environment where a compiler is unavailable, and no pre-built binaries can be installed? 
Alternatively, is there a pure-python numpy implementation?