Service-oriented requirements elicitation emphasizes understanding and addressing stakeholder needs. As a critical phase in software development, it relies heavily on clear and effective communication with stakeholders. One valuable tool for facilitating this communication is the questionnaire. However, the challenge lies in the fact that there are an infinite number of potential questions that could be asked. Often, critical questions are forgotten or omitted, leading to incomplete requirements. Additionally, wrong questions or poorly phrased questions can result in incorrect requirements. To address these challenges, we leverage GenAI to identify well-written, critical questions. In our proposed Problem-Driven GenAI Requirements Elicitation Process, question formulation and requirements gathering are systematic, iterative, incremental, and interleaving. Our approach focuses on the four key dimensions of Requirements Engineering (RE): Functional Requirements/Non-Functional Requirements, Problem/Solution, Product/Process, and Stakeholder. Taking the cross-product of these four dimensions, we delineate 24 distinct sectors. In order to ask the right questions and the right number of questions, we use GenAI to conduct experiments that systematically generate questions across these sectors. This process helps uncover critical questions for the development of Theia, an indoor navigation system designed for visually impaired individuals. As part of our evaluation, we compare student-generated questions for Theia with those created by ChatGPT 4.0, under the guidance of Requirements Engineers. The questions are then assessed based on desirable properties of questioning. In our limited studies, we find that our problem-driven GenAI approach reduces the occurrence of omitted and wrong questions by 54.45%, depending on the sector. We believe this approach is important as it helps narrow down the infinite number of potential questions and helps address critical questions.