HDMI port not working

If your MacBook Air has no MagSafe port, and one of the USB-C ports is broken, your options are to:

1. Charge the MacBook Air using the USB-C port that still works. You may want to use an external dock that has support for pass-through charging power so that you can connect other stuff to that remaining USB-C port at the same time that you are charging the notebook.
2. Have the notebook repaired so that both USB-C ports work. (See Mac Repair & Service - Apple Support)
3. Replace the notebook.

What HDMI ports? An HDMI port is a video output port of the type used to connect to HDTVs and some monitors. Some MacBook Pros have them, but as far as I know, no MacBook Airs ever have. Furthermore, you would not use HDMI ports for charging.

Did you mean to refer to a USB-C port?

Can you charge your MacBook Air via the MagSafe charging connector?

Regarding the inability to charge via USB-C, can you provide details on what cable/power adapter you're using?

Also...does charging work on a different USB-C port on your MacBook Air?