Maybe this will be of some help.
First of all, I have never worked on a Toshiba laptop, nor have I ever seen that problem on any laptop. Therefore, these comments are more conjecture then actual proven facts.
The laptop ahs internal regulators that reduces battery voltage down to a level that is suitable for the laptop. When you plug in a charger, the voltage jumps way above the level of the battery. That is necessary in order for the battery to charge. Now it's theoretically possible that the regulators on the motherboard of the laptop can no longer adjust to the higher voltage that is normally present for in the charger.
As I said, this is being stated without any proof that that ever happens. A more plausible explanation is that there is something wrong with the charger and it is putting out far too much voltage than it should. The laptop has internal devices that prevent the battery from being overcharged.
That is the best I can possibly offer. My recommendation is to not try to use the computer while you have the charger plugged into it. Also, you should verify that the charger is putting out the correct voltage for your laptop. Even if you are sure it is the original charger, there is the possibility a component in the charger could fail in such a way as to increase the voltage output. Although that may seem unlikely, it is not. In theory, at least, a component failure could cause the charger to put out more voltage out than it should.
The cost of preparing your laptop may be more than you are willing to pay. Also, it could be, there is something wrong with the display, even though that seems unlikely. According to the information you have provided.
The best solution may be to contact Toshiba and find out what services they have available for you and what options they will give you.
Toshiba is one of the big makers of laptop computers and we would expect they take pride in their equipment. They may wish to do you a favor and offer your replacement Toshiba laptop for the wholesale price. Just a possibility.
