Sometimes, you need to learn to say no, and sometimes, you need to trust people. Unfortunately, I've been burned a few times by people "promising" money coming in, but never got around to it. It's happened 3 times, with different clients. I now ask for at least a DEPOSIT up front.
Let's assume they can secure the investment after your meeting. How long do you propose your meeting is going to take? How about any work you need to do at home calculating costs? You'll need to be an expert at estimations, which can be difficult.
Let the client know you will be charging for the initial meeting at xx amount per hour. You are setting aside up to y hours to talk to them, so that initial cost will be $ zzzz. Let them know that if it takes less time, they'll get a lower bill for that part only. I would also recommend going in prepared with all the questions you'll need answered, and knowing not to give the end completion date unless you have all details, and a deposit is paid.
Luckily, short meetings for getting the scope of the project won't kill you, as long as you limit how much time you're spending on it. An hour here or there will add up, but you sound like you have enough work to cover those few hours. But you need to set the precedent that you need paid for your time, otherwise you'll seem like a kid off the street.
Questions you may need to ask should be written down, so you can ask them, right down the answer, and move on. Ask the client to do the same thing. They should have:
- The project scope (and goal).
- Are the assets already obtained/easily obtained? (i.e. images, servers, licensing, etc)
- A drawing of the layout they want.
- Easy-to-follow diagrams that explain what each function is they want to implement (i.e. Click the Widget button, and bring up the Widget Item Entry form).
- All the above should be on paper, not just emailed. Leave room for writing notes.
If the client does a majority of the above work, your initial meeting will be short (saving you time, and potentially money if they don't pay as expected), and sweet. As well, it lets you get to the programming aspect, which I assume you enjoy a lot more than drawing pictures and writing questions.
If you can contact your client ASAP about what you need from him, and explain that it will help move the project right along, they should respect you for it, and also show they are willing to go to the investors and actually fight for the money... Mentally, I mean, not physically. It will help separate the freeloaders from the people who actually want it done, and are willing to pay for it.
