Actually, I think because he made an initial payment you are entitled to the full amount. The first payment is acceptance of the agreement and legally I believe you can claim the entire amount. I'm not positive. You would still need to do all the work, though.
Time IS money and the logo alone is probably worth more than the $80 he paid you. I feel bad if the kid has financial problems but maybe this is a lesson in life.
Now, I will go to the BOI and refresh myself on what that complaint about you was