Sorry it didn't work out :/
Yeah, I wouldn't offer to lower the hourly rate when negotiating after you've tried to start on a contract. It feels weird if you haven't worked as or with a contractor before, but you have to treat time working on the problem, whether actually programming, communicating with the client, outlining stuff on paper, or whatever, as equally billable and valuable and track it all carefully, and not sell yourself short. In a professional setting, even if they don't like the work you did and you're total crap at it, they are supposed to still pay you for your time. (That's why you want to communicate with them regularly; it gives them outs in case they get cold feet, and ensures you're more likely to get paid for time you actually spent. You can refuse to do work on the next phase until they've paid you for the work you've done so far).
When you get a whiff of hesitation from the client side, it's usually an indication that they aren't very experienced hiring programmers/contractors in general, and you'll want to be wary of completing tasks in good faith; often you just won't get paid at the end.
The other option is to negotiate a flat fee, of course. That gives you more leeway if you aren't confident in how long it will take you, but it puts you on the hook if the problem is harder than first advertised, and the client might decide to add additional requirements and expect you to implement them without any additional payment.
To find work you could try a middle man site. I think I looked in to
Guru once upon a time, and it looked legit. There's probably some other similar sites. It makes it easy to find projects of a small enough scope that you feel you can complete them and get your feet wet. There's the added benefit that sometimes the site will handle the actual payment from the client, or even keep the cash in escrow. Even if you go it alone, finding someone to escrow for you might not be a bad idea.
I guess my primary message is: be really paranoid about getting paid and keeping the client informed (and having them inform you). I've heard a lot of horror stories about people doing work for a client and not getting paid. Most people aren't good at communicating what they want, and when suddenly the price tag is a hundred dollars or more and the prototype the programmer shows is terrible and not even close to what they want, most people panic and try to just pull the plug on the whole thing and forget it.