PhD admissions committees at strong departments are looking for clear evidence of potential for high-quality independent research.
Test scores only matter if they're low. In particular, if your math score is low, there will be serious doubts about your math ability, and if your verbal/TOEFL score is low, there will be serious questions about your communication skills. In some departments (like mine in CS), admission to the PhD requires a TOEFL Speak score above a certain minimum (in my case: 22), because all PhD students are expected to be TAs at least once while they're in the program, and the state of Illinois requires a minimum Speak score (in my case: 24) on TAs who are not native English speakers.
Publication records only matter if the papers are either good or horrible. It's utterly impossible to tell from the number of publications whether the applicant has significant promise for future independent research. High-quality papers, written in flawless English, published in well-known venues that are easily accessible online from the US, are definitely helpful. Poorly written incremental results in the Inaccessible Khazakhstani Journal of Computer Stuff is at best meaningless and at worst actively damaging.