If your charger outputs 19VDC then disconnect the battery and plug in the charger to see if the computer will turn on. If yes then replace the battery.
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If you have never openned up a computer before then proceed very slowly being sure to not to short out anything. Touch as little as possible.
Could be a number of issues. Dead battery, defective charger or the charging plug is loose or even the power outlet on the wall is not working..
Is there any charge left at all in your battery? Will it turn on at all?
Test the power outlet with a lamp or something to see if it works.
Do you have a multimeter to check the charger? It should be around 19VDC.