Yes, exactly see if it will run on AC power only. If it will then theres a good chance that when you put the battery back in it will start working normally again. IDK why but for the last 15-20 years its been an uncommon issue where the laptop for whatever reason gets "stuck" for a lack of a...
If you're up to the task, Take the bottom off of the laptop, remove the battery and plug it in to the AC adapter and see if it will power on. If it does power on then turn it back off and put the battery back in it, plug it back in to the AC adapter and see if it will start up and charge then. If...