If you know the idea can work, than a limited/non-existent marketing budget shouldn't stop you and it certainly shouldn't discourage you this much.

It sounds to me like you need to dig deeper, both into getting more funding and reviving your motivation. You've come this far. It seems a foolish idea to me that you would consider pulling the plug becacuse you lack cash for marketing.

Cash can be found. Keep at it. Perseverence is hard and success has peaks and valleys. Just because you're in a valley right now, doesn't mean it will last forever.