Joe has it right. Don't worry about sounding "crude," as you put it.
Just ask. These questions may best be answered by a business person, not an HR person, but that depends on the people. This is business, and startups are risky business. It will help your case in your interview process if you ask questions that show you care about the company's situation.
You can say something like this.
"Please tell me a bit about your company.
"Where are you getting the cash for payroll and other expenses? Please tell me a bit about your investors. How long is it until you need another round of financing?"
You can even ask these questions:
"Who are your competitors? Do you have any key customers lined up? What are the critical success factors in succeeding in your business? What do you expect me, personally, to do to help make the company successful?"
The "what do I need to do?" question is important: it shows you understand that you're a part of the company's success.
Don't be the slightest bit embarrassed to ask these questions. You won't annoy any serious entrepreneur by asking them. Quite the opposite.
If you get evasive answers, especially about the company's investors or financing plans, you need to be very careful about the job.