Won't turn on. Bought a new charger - it's light is green, but the laptop blue charging light does not come on. It was left plugged in and no power has been restored. What should I check? What are the possibilities? How can they be resolved?

MF. Could be the new charger is faulty, return charger for exchange or refund. Battery could also be faulty, have it tested if you can by a computer tech. Check the attached links,instruction and guides, Good luck
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My laptop notebook will not turn on
my asus laptop wont even charge or turn on after it shut off mid windows...
Laptop Won Come On Even When Connected To Charger
Why Won My Laptop Turn On Even Though It Plugged In

please see the commentary. God bless you

• 
  The majority of laptops will display a solid green, blue or purple battery light to indicate that the battery is fully charged. Most manufacturers indicate that a laptop is in the process of charging by displaying a solid or blinking green, orange, blue or purple light. If your battery indicator light is green, blue or purple, the battery is probably functional, regardless of whether the light is blinking. If the light is solid orange, the laptop is probably in the process of charging.
  
  

Battery Error Coneventions

• 
  Many battery manufacturers use rapidly blinking lights to indicate that a battery's charge level is low. In general, a laptop will rapidly blink orange or red when its charge drops below a certain level until the computer is plugged into a power outlet and charged. If your laptop's battery indicator continues to blink rapidly in orange or red or if it remains red even when it is plugged into the charger, it indicates a problem with your battery or the charger.
  
  

Read more: http://www.ehow.com/info_12183593_blinking-battery-light-laptop-mean-charger-not-charging.html#ixzz2fu5qhEWg

please read and execute the commentaries. God bless you
Charging Conventions

• 
  The majority of laptops will display a solid green, blue or purple battery light to indicate that the battery is fully charged. Most manufacturers indicate that a laptop is in the process of charging by displaying a solid or blinking green, orange, blue or purple light. If your battery indicator light is green, blue or purple, the battery is probably functional, regardless of whether the light is blinking. If the light is solid orange, the laptop is probably in the process of charging.
  
  

Battery Error Coneventions

• 
  Many battery manufacturers use rapidly blinking lights to indicate that a battery's charge level is low. In general, a laptop will rapidly blink orange or red when its charge drops below a certain level until the computer is plugged into a power outlet and charged. If your laptop's battery indicator continues to blink rapidly in orange or red or if it remains red even when it is plugged into the charger, it indicates a problem with your battery or the charger.
  
  

Hello! It seems that you have a problem with the laptop charger connector. It maybe in short circuit. You can try to look for some electronic workshop that works with reballing, BGA solder, etc., that might change it. In Portugal we have some, so I think in other countries you can find them to.

This is a common problem. It may be that the charger is dammaged. these Dell chargers have a micro thin communication cable in them that tell the charger to charge the battery. this micro thin cable can often break. Its use it to prevent the laptop battery from over charging, but if it breaks or becomed broken inside tha charger cable, then the laptop simply won't get the charge signal and the battery won't charge. If this is the case, then you will need to replace the charger with another Dell charger compatible with your laptop

If the laptop battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced.

The first thing to do is check that the charger is putting out the correct voltage, which should be ~18 volt. Then try to start it without the battery.
If your voltage is OK and the battery out makes no difference, then I would suspect that you have a motherboard problem that must be fixed. If the computer starts up if you wiggle the DC plug where it goes into the computer, then it's the DC jack that is looks and must be re-soldered.

Please refer to the following article for a detailed diagnosis & suggestions for fixing this issue:
http://www.fixya.com/support/r6395191-troubleshooting_laptop_power_failures_ac

The brand new battery needs to be charged completely at the very first time you start to use it.

It sounds like defective power jack. Bring it to a reapir shop.