When troubleshooting a Macbook Air, there is a checklist from Apple Support you need to try.
You are welcome to do so after first trying these steps first.
• Check the Magsafe power adapter, to make sure it is free of debris and is seated properly.
• If with decent charge, try to start the Macbook Air, with only the battery.
If you get power from either one of these issue resolved- otherwise follow the steps provide more in detail from Apple listed in the link below.
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Apple Support Link:
Troubleshooting Macbook Air (additional steps)
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Such power issues with Macbook Airs as well as Macbook 13" and Macbook Pro 13" are about the same and there are no workarounds, so make sure to follow those procedures completely for a full assessment of your Macbook Air's functionality.
Hope this helps!
Regards,
-Mactechtrainer