Unfortunately it is hard to say what is wrong with the laptop and after sitting so long you may actually have two problems. The original problem and now a dead battery that may be preventing the laptop from powering on or booting.
Unless you know someone familiar with working & troubleshooting Macs, then your best option would be to remove the SSD and put it into an OWC Envoy Pro Enclosure so you can connect it to another Mac to attempt to access the data on it. You will need to know the exact model of your Mac since the 2013 model had two versions an Early and Late 2013 models which use different types of proprietary SSD connectors.
You can get the exact model of the Mac by entering the system serial number on the check coverage page here (please don't post the serial number on the forum since it is considered personal information):
Check Your Service and Support Coverage - Apple Support