Don't start with a lawsuit. Let that be in reserve if you need it, but don't start with one. That's like offering 100% of what you'll pay on the first negotiation with a car dealer. You need to keep something in reserve.
Try your contact again. Use phone, email, snail mail, etc. Use every single means you have to contact that person. If you have a snail mail address, send the letter via registered mail so that the contact must sign for the letter. In that way, you have proof that it was received.
Demand payment. Send a copy of your time slips, invoices, receipts, whatever is involved with being paid. It doesn't matter if you already sent them. Send them again.
While you are pursuing this line, check out the Hawaii BBB. See:
http://www.hawaii.bbb.org/ and also get contact information for whoever you can in Georgia. Also, see if you can get any information on any supervisor the Arizona person has. If the first route does not work at all (e. g. working directly with your contact), you will need to go the route of either contacting Georgia or the Hawaiian BBB, or the Arizona person's supervisor. But try your recruiter (I suspect that is who your Arizona contact is) first, and give him or her the opportunity to fix the problem.
If all of these methods fail, the next step is to make a stink about suing. But try the "friendly"/first line approach first. It's possible that paperwork was lost or the Arizona person may be waiting for payment from Georgia. This can happen with contracts, but keep in mind also that recruiters can also sometimes skip town with payments that were intended for contractors. Protect your interests.
Best of luck to you.