Hourly Contracting Problem? Can Only Bill Limited Hours with Client

Since you are just employed by the company and not a founder/shareholder, then your question is not startup-specific. Given your current situation, working for a low salary in exchange of a lump sum of money in case they succeed and sell the company does not make sense. I'd say if you're not happy with your work and/or salary just go and find another company, startup or not.

I am contracting (pay by hour)

That says it all - as Jordi C. stated, this question is not startup specific.

Contracting means this: when the client has work for you, you perform the work, and you bill them for the actual time that the work requires for you to do. It doesn't matter whether there is work "forsaken" that they do not give you to perform. You didn't get the work so you don't bill for the time.

The biggest single problem I see in your present situation as a contractor may be this:

I just work less than 8 hours a week.

Legally, everyone is OK here. They ask you to do work, and you bill them.

The real problem will be the expectations of the client. They may expect you to hang around on standby while they decide whether to farm work out to you every week.

If you are being asked (told) to be in their offices during their work hours all week while they determine if they have things for you to do, then this arrangement is exceptionally bad for you.

Normally, on site contractors in IT are paid for all time they spend on the client's site.

If you are off-site and you can determine your hours and other work that may come from other clients, then what you describe is an OK arrangement. And you are not being abused if this is the working arrangement.

Many contractors work on an "as needed" basis, and they have several clients that they juggle.

If you are asked to hang out in their offices even when you are not billing, then you absolutely should not be doing this. Doing so is a waste of your time and it is somewhat like slavery or "day labor", since you probably can't attend to your other projects while you are waiting for them to assign you work.

So, the course that you should take will depend upon what the client is asking. The bottom line is this: if it is up to 8 hours a week but you determine your own work availability and you can do unrelated things with your time between their projects, it's fine. If you must stay available all week in case they need you, it's a bad deal and not proper.

It depends on what you're trying to get out of the experience. Are you approaching this as a just a job where you want to be a 9-5er (albeit a contractor) or are you doing it for another reason, like learning about the startup world / trying to get in on some of the action?

It sounds more or less like you're a paid intern, or at least are being treated like one. If I was you, I would come up with a 1 year plan and see if that company can give you what you're looking for.