Your computer has two batteries, the main battery and a real-time clock (RTC) battery.
Advocate that you download the HWiNFO software from
https://www.hwinfo.com/download/. Install and run HWiNFO to collect your computer profile. Have a look at the computer's smart battery status and the current power status in particular. Also look to confirm that the AC Adaptor is charging the main battery.
Not sure if your computer supports "hot swapping" of the main battery pack. Usually completion of POST is required so that the computer recognises the main battery during start-up.
However
Toshiba's P700 Series User’s Guide says Place the computer into Hibernation mode and replace the main battery pack with a charged spare. It also says If the AC power light flashes amber during charging, either a battery pack is malfunctioning, or it is not receiving correct input from the AC power supply. Hopefully HWiNFO has also given you this diagnostic information.
Toshiba's Knowledge Base also has information on battery not taking a charge, etc.
I guess that this computer's warranty has expired, but there is nothing to stop you registering your Toshiba and asking for online technical assistance.