For anyone out there who might care.
Problem: The initial problem was that the Toshiba laptop would work fine on battery but crash when a charger was plugged in. On further exam, found that laptop would crash when battery reached full or close to full charge. Fault probably '''REappeared''' after an update.
Fix: Disable the system processors in Device Manager. You need to be in safe mode to disable the processors. Then reboot.
This stops the power functions from running for your processors, which is what was pulling down the unit when a full battery charge was reached. These features are not absolutely needed, it just means that the system uses more power and can be a little slower.