Laptop switching to battery while connected to AC adapter

Laptop switching to battery power while turned on with AC adaptor
Model: Toshiba Satellite A70-TS100E
I was wondering if you could help me in identifying the cause of this problem.
While turned on, the laptop will switch to battery power even if connected with the AC adaptor (sometimes during boot-up, or after a while) until the battery drains out, he then goes to hibernation (the battery light is off). If no battery in the laptop, it will shut down, and the AC light will blink very fast. The battery (li-ion) will only charge up to 10%, where it then jumps right up to 100%, and will discharge from 100% to 90% then jump to 0%, go to hibernation, and fails to complete the process, shutting down. The adaptor makes a small “camera flash charging” sound, stabilizing at 19v. When charging, it repeatedly makes the “charging sound” Faulty AC adaptor? Or Faulty battery? Or Both?

I think you might have a few different problems at the same time.
First problem: the laptop switches to battery power even with connected AC adapter. Most likely you have a faulty power jack. It’s either broken or loose. It’s a known issue with Satellite A70/A75 laptops and you can fix it by replacing/resoldering the power jack or relocating it outside laptop case.
It also could be a problem with the power cord. Find a multimeter and check the AC adapter. See if the power cuts off when you jiggle the power cord. If it does, replace the adapter.
Second problem: the battery will discharge from 100% to 90% and then jump to 0%. It sounds like a bad battery.