The Mac Mini takes 18 volts input. Check out the discussion on the Carnetix
forums or look at some of the early threads here about powering the Mini.
Seems like by the time you've bought a laptop iBook adaptor and hacked it up and tried to add a battery system from an iBook, maybe it would just be easier to either buy a used iBook or spend an extra $30 on the P1900? You'd get engineered regulation, auto startup/shutdown, and filtered 5 volt output for your USB.
Not trying to discourage you. By all means, if it's the journey you're interested in, that's cool. Otherwise, it seems quite a long way to go when a ready made solution is pretty close in price. The extra $$'s are pretty cheap labor for a polished product.