Hello Dglesner
There can be a few ways to diagnose and isolate the issue before you begin rectification.
> Plug the charger in and check if the charging light (the indicator) lights up.
> Try turning on the laptop without the battery, i.e. only by plugging in the charger.
> Check if the CMOS battery of the laptop is faulty (by taking it out and then powering the laptop on).
> Check if any of the RAM is faulty (by taking it out from its slot one at a time and powering the laptop on).
If none of the above methods show any life in the laptop, you should take it to an authorized service center for proper and professional diagnosis.
Hope this helps. Good Luck!!