MacBook Air Start up Issue

First, try and reset the SMC

Reset the SMC of your Mac - Apple Support

If this is not working, charge the MacBook for a prolonged period of time to see if this is fixing the issue

If not, follow the steps provided in this article: If your Mac doesn't turn on - Apple Support

Hi,

Resetting SMC could solve the battery related issues.

Reset the SMC of your Mac - Apple Support

I just wonder if you did charged battery after replaced it.