Hey!
Same situation here
Actually, I was in the same case last year, but for the MS program. I was admitted, but none of my professors of interest had funding available...
Finally, I went somewhere else. Yet, I believe that professors are more interested in PhD students than in MS students, so this might be good for us!
Personally, I contacted only a few professors in a precise area (two or three). If none of them is interested in my profile, then maybe I will broaden my search.
Anyway, good luck!