While I agree with most of the responses to your situation, I'd also suggest this.
How much do you believe in the start-up?
How much do you want to work there?
Personally, I'd have a VERY frank discussion with the founders about the current situation. They should respect what you are giving up, and be concerned about putting you in a difficult situation.
Who knows, they may suggest that you hang onto your current position and circle back in a few months once they have funding. Maybe they offer you more equity for greater risk. Maybe they're flippant about the effect this change may have on you and ignore the risks.
Whatever the result, you'll get a better feel for where they are at, and get some answers to your current questions.
If they can't be open and honest with you now, or you feel they aren't being, would you still feel safe with the move?