Does the system recognize the AC adapter, or is it showing unknown?  F2 at powerup to check.

Assuming that you are referring to the 2010 Latitude E5410 "Battery Status Lights ", page 22?

* Alternately blinking amber light and blue light = An unauthenticated or unsupported non-Dell AC adapter is attached to your laptop
* Alternately blinking amber light with steady blue light = Temporary battery failure with AC adapter present
* Constantly blinking amber light = Fatal battery failure with AC adapter present
* Light off = Battery in full charge mode with AC adapter present
* Blue light on = Battery in charge mode with AC adapter present

Try this =

* Disconnect the AC adapter from the laptop
* Remove the battery from the laptop
* Press and hold down the laptop power button for 10 seconds
* Reconnect only the AC adapter to the laptop
* Press the laptop power button
- If the laptop powers on, the AC adapter and power port are functioning
- If the laptop does not power on, either the AC adapter is faulty or the power port is faulty

* If the laptop powered on in the previous test, turn the laptop off
* Disconnect the AC adapter from the laptop
* Press and hold down the laptop power button for 10 seconds
* Reinstall the battery into the laptop
* Reconnect the AC adapter to the laptop
* Press the laptop power button
- If the laptop does not power on, the battery is faulty