Call me skeptical, but I don't believe the "client" intends to or will ever pay for any of the work.
Rocknbill has a good point, you probably had a chance to establish a *relationship* with the client, esp since they asked you to do the extra IT stuff. Would have been a perfect occasion for you to step up to the plate and see what else you might be able to help them with.
My guess is that this client initially wanted you to be more involved overall, and did not communicate this clearly enough. You, on the other hand have let the ball drop by not getting in touch regularly and not being proactive enough in trying to understand their needs vs their explicit wants...
To late to fix now, focus on paid work - forget "getting revenge" get better new clients instead.
Not walking away is called "loss aversion" or the Sunk cost fallacy [en.wikipedia.org]