hp 15r108nl won't boot without battery

I have an hp 15r108nl that  won't boot without battery. I try to explain myself better.

If I boot the laptop and then i remove battery it works properly.

Also if i turn off my lapton without disconnect the AC adapter  I can boot it ( without battery).

If i turn off my laptop and I disconnect my AC adapter and then I connect again, my laptop won't boot without battery. The blue light near the connectors does not turn on.

This is a very odd behaviour.

Thanks for help