I need a cheap power source (max $10 cost) that will output 12v 1A. It will use any kind of batteries you want, we prefer lithium [url removed, login to view] or 4 AA batteries. It will step-up the battery power to 12V for the output. The batteries are rechargeable and will recharge with solar panels (it's up to you how many, but remember it's a cheap project, customers won't consume a lot of energy and system will be on stand by more than 90% of the time). It would be good if the solar panel input were something like a 5V DC jack.
12V <--- Step-UP <--- Batteries <--- Controlled Charger <--- 5V input <--- Solar Panel