PSP won't turn on while charging with battery inside, also won't after a day of not being used.

[/psp]

Hi everyone, I recently wanted to use again my old psp after many years.
I bought a battery on ebay, and when I plugged it in it didn't turn on right away, I had to use the charger and I noticed right away that when I tried to turn the psp on the console tried to turn on for a second and then crashed. I thought maybe the battery was without power so left it charging.
After a while I tried to turning it on without the charger and it did, played a while and it was fine, then turned it off for some hour and when trying to play again saw that the battery was being drained while not used, but didn't mind.
The day after the psp didn't want to turn on like the first day, had to charge for a while and then I could play. This loop has going on so far.
What could be the problem? Simply the battery being bad?
(sorry for my english and poor use of words btw)
submitted by /u/Sunburn17
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Source: https://www.reddit.com/r/PSP/comments/1 ... h_battery/