How to proceed if a professor does not answer the request for letter of recommendation?
What it means depends a lot on the proximity of your application deadline.  If the deadline is looming, say, within ten days to two weeks, it means you should probably ask someone else.  If the deadline is a month or more away, it means the professor is busy.  (And, if you didn't tell the professor when the deadline is, it means you didn't provide enough information.)

Send a polite email that tells when the deadline is and asks whether the professor could write a recommendation by that time.  That should get some kind of response, even if it's, "Sorry... I'm really busy right now and cannot do it."

Here is my general advice to students about recommendations: http://ksuweb.kennesaw.edu/faculty/rbrow211/recommendations/ It will likely help you to read it all, although the bit about communicating deadlines is the first item on the list, in bold type.