I have a toshiba satellite A205-S4617. The battery

the laptop overheated and the motherboard is damaged and need replaced

Toshiba laptops are notorious for this problem. I see at least 20 of these a month.

If the power light continues to just blink orange and nothing else works, the power module board has failed. You can send it off to most laptop repair facilities, but I have also found if you call toshiba repair center and make enough fuss, they will repair it for a reduced fee, because it is a design fault. They know all about the problem, and will immediately tell you to send it in. That's when you let them know you have found it is extremely common to the satellite's

If you connect the ac adoptor to your toshiba notebook and if it worked, then the problem is on the internal battery PA 3534U-IBRS. It is not the power cord or overheating the laptop, but the battery itself that is not capable of charging power from source anymore. If your laptop is still covered with warranty period, you can contact your provider or the outlet for service and replacement of your battery. However, if it's already due, then you can order the said battery to http://www.toshibadirect.com/td/b2c/findBatteries.jsp and that will cost you $129.99/$149.00 for the replacement.
Bless you.