I have a Dell Inspiron N5510. It was plugged into the wall with the charger while the battery was in as well. We were surprised when the battery died. Since then, I have been unable to get it to turn on. 

When the charger is plugged in, the charger light is green. once it is plugged into the computer, the light goes out and it will not charge the laptop. I have tried other chargers with the same results and the battery was fine before this. 

From my research, it sounds like there is an electrical issue and I most likely need to replace the motherboard. I have several questions for anyone who can help. 

Is is it worth it to replace the motherboard? 

What motherboard do I need for this laptop?

What is the likelihood that the information on my computer is still safe? 

Is is it possible to save this laptop or should I just give up  on it?

Any information would be greatly appreciated. Thanks!!