Hahaha yes, your solution follows the common sense, but I'm not trying to replace my car stereo with the boombox, instead I'm making a portable music player for outdoor parties.
Check my blog below, is in spanish but google translatin can make the trick. Is the entry of the SONY Boombox, with blue speaker caps.
Offcourse there are a lot of better IC's and custom PCB's for portable amplifiers, but as you may see, the objective of my site is reusing existing equipment, and adding new functions to the old one.
I'm gonna use the Eric's solution, with two 12 volt 7 amp/hour batteries and LM7805 - LM7905 regulators. Small but very heavy, I see no other solution.
Thank you so much guys for your answers! Very clear and professional, even for my simple problem.