Macbook Pro won't turn on without charger conected

Disconnect all external devices

Reset the System Management Controller (SMC)

https://support.apple.com/en-us/HT201295

repeat 2/3 times

Reset the nonvolatile random-access memory (NVRAM)

(OPTION+COMMAND+p+r at Startup)

https://support.apple.com/en-us/HT204063

repeat 2/3 times

Then use safeboot (SHIFT at Startup)

https://support.apple.com/en-us/HT201262

Then reboot normally with devices disconnected.

Determine battery cycle count for Mac notebooks - Apple Support

If resetting the SMC doesn't work, then you more than likely have a battery issue. When I read your post, that's where my mind first went. If the SMC reset doesn't work, I would take it to an Apple store or a third-party AASP (Apple Authorized Service Provider). A safe boot isn't going to do anything for you in my opinion.

JimmyCMPIT wrote:

Determine battery cycle count for Mac notebooks - Apple Support

If the battery is completely dead, it's not going to report anything except "no battery" or something to that effect.

and that result might be important if the OP responded that's whats showing.