Usually we would all suggest to install [link|https://www.coconut-flavour.com/coconutbattery/#plus|coconutBattery] to see the batteries status, but seeing that it no longer powers up at all then it suggests that their is an issue along the power rails on the logic board which would require a skilled technician with the know how and available parts to replace. Replacing the battery itself isn't impossible when following the guides carefully, but it is still worthwhile as these units are still worth more than the the cost to repair. At least I would search around for a local repair service to get their price and opinion and go from there with your decision.