PSP 3006, working but couple of issues, read description

PSP 3006, working but couple of issues, read description

Selling a Sony PSP 3000-series (Model 3006) in good cosmetic condition. The body, screen, and buttons show minimal wear and look good for its age. ( my opinion only, judge for yourself with pictures)
Issue 1 : it seems to only power on when plugged in with a wall charger, I don't think it is a battery issue because I tried with 2 different batteries that i had without luck, Issue 2 : umd drive a bit noisy when launching games but it works fine,
On start up sometimes the console takes a little while to launch main menu, not sure why., I find opening umd drive and closing again straight away make things faster., When plugged to the wall the charging end bit doesn't always stay on the console when moving which can disconnect from console sometimes.
Included is console unit only ! With battery which I believe is pretty new,
No charger included