please have a look to my pictures - logic board - battery not loading

It's very very unusual that due to a bad DC-in an iBook would work fine on AC power but not charge a battery. iBook DC-ins pretty much either work 100% or they don't work at all, so it's very unlikely that the DC-in is the cause, if the laptop works fine on AC power. It's also very rare for battery connectors in iBooks go bad.

Before doing anything, test your machine with a known-good battery to see if the behavior changes. Test with several batteries if possible. iBook batteries are very flaky and can misbehave in a million different ways, and 99% of the time the battery itself ends up being the problem. I would hate to see you spending time and money on repairs when most likely that is not even the issue.