The problem could be related with your power adapter or your battery. On your power adapter, The first component to check is the 2 cords one that connects to the wall and adapter to computer. If the computer doesn't start whit the battery on, the battery is faulty.
Please follow our troubleshooting page. It can help you to check what is causing you problems.
[[Toshiba Satellite 1415-S105 Troubleshooting]]
Also, you can check our guide to see how to replace your battery.
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