If the battery has become completely discharged it can prevent the laptop from charging or even powering on. You should never let the battery become completely discharged for any length of time as it can permanently damage the battery.
Try an SMC Reset. Keep an eye on the Magsafe LED when performing the SMC Reset to see if the LED changes color (should go out, then green, then amber if it needs to charge the battery).
Try unplugging the charger from the electrical outlet for a minute to reset the charger's internal circuitry. Also check the Magsafe connector and port for damage or any foreign object such as a staple or other small metal object stuck within the Magsafe port preventing the Magsafe connector from seating properly. Here is an Apple article for troubleshooting Magsafe charging issues:
https://support.apple.com/en-us/HT203207
If this doesn't work, then the battery may be preventing the laptop from powering on. A lot of times if you disconnect the battery and use only the charger you can get the laptop to power on. If the laptop powers on, then try reconnecting the battery while the laptop is still booted and let the battery charge at least 10%, otherwise the battery will become permanently damaged. You need to be extremely careful not to let any metallic or conductive item or surface make contact with any of the internal electronics otherwise you may damage the laptop. If the battery won't charge after giving it lots of time then the battery is most likely bad. If the laptop won't power on with the battery disconnected and you tried everything else listed here, then you likely have some other hardware issue with the laptop.
Your laptop is considered "Vintage", but it may still be possible to have the laptop repaired by an Apple Authorized Service Provider if the necessary part is still available.