troubleshooting order:
# Verify the charger is OK by measuring the voltage or plugging into another similar computer.
# Verify the socket of the computer is clean and not broken.
# Remove the battery and plug in the charger. Most LT will run with just the charger. If it does, that would indicate a battery issue.
# If none of that works, you will have to open it up, repeat #2 and verify all the cables are secure - disconnect them and reconnect them. Be careful, those connectors are easily broken if you don't open them properly. Search for how to do it for your connectors.
# Panic - at this point it is either the power PCB, if there is one, or the MB.