Increase chance of reply when e-mailing an eminent researcher?
Your chances of a reply will correlate quite strongly with two factors:


How interesting your problem is.
How long it will take the professor to respond.


Thus, you should:


Make everything as brief as possible, yet still include all necessary information. 
Ask yes, no, or short-answer questions that the professor will know off the top of his/her head. Ask for references to a paper, or for whole pieces of code: not the embedded details.
Briefly mention that you're a PhD student at Fake University, supervised by Professor Jones (if the prof you're contacting likes your supervisor's work, that's a good start).