For $29/mo, we provide access to advanced level technicians who will answer your questions on any Macbook board related matter to the best of their knowledge promptly & walk you through how to solve your problem so you can deliver a working board to your customer.
Check what the battery reports with CoconutBattery for OS X or a test with ASD if the model you have has one. Maybe the internal diagnostic test will report a back battery as well but I'm not 100% sure.
(You can run CoconutBattery on a Guest Account by opening it from the Terminal if you don't have the customer's login)
I assume the board looks ok and you're using an original charger?
worth to order the battery, even if it turns out not the battery is the issue, u will have a spare one, that model wont turn on without the battery, so u can use it for the next troubleshooting. Not charging over 30% is likely the battery though.