Chances at funded cs PhD with high GPA and GRE scores but no research experience or professor connections?
Your big challenge—and this would be true regardless of the field—is that you have no "professor connections." This is a major challenge for you, because one of the most important parts of a graduate application is the letters of recommendation. If you don't have people who know you and can vouch for your capability to be a successful graduate student, you're going to have a tough time getting admitted to a graduate school, and especially top-20 programs.

The good news is that in most science and engineering graduate programs, if you do get into a reputable program, you should be able to get a guarantee of funding (either as an RA or TA) for the length of your graduate career (assuming you make "normal progress" and are a good departmental citizen, etc.). I would be leery of accepting an offer from a school that doesn't make such a commitment!