To start make sure the battery is completely secured just to be safe. The batteries on this laptop are tricky and sometimes require more then just "popping them in." Try following the battery replacement guide on the device home page to make sure it fits in properly.
Try plugging the laptop in to charge and leave it for a couple hours. After that try turning it on by holding the start button.
If that did not work then check the charger. If you have another charger try that as well, or if you have another device that the laptop charger fits into, try that as well.
If none of these solutions helped the battery may need to be replaced. Try the troubleshooting page to help narrow the problem down.
Troubleshooting page link: [[Satellite C55-C5241 Troubleshooting]]