There is no air coming from air vents after replacing the battery?

The first thing I would do is check the fuses, there is no vacuum to control the HVAC system so the problem must be electronic. I have seen the programmer go out and cause this issue, here is how to run the codes to help see what's going on.

Please go over this guide:

https://www.2carpros.com/articles/low-or-no-air-flow-from-vents

The HVAC programmer contains "self" diagnostics that, when accessed with the scan tool, are designed to identify the source of any system malfunction as specifically as possible, including whether or not the malfunction is current or the non-current (history) type.

The letter "H" after any of these DTCs indicates a history code. Example: DTC B1310H = History.

Displaying Diagnostic Trouble Codes (DTCs)

The diagnostic trouble codes (DTC) set by the HVAC programmer can be displayed by the "On-board" method.

1. Press and hold the "OFF," "AUTO," and "RECIRC" buttons for one second.
2. The DTCs will display for two seconds each, and then return to normal operation.

Here is more information on the system, check out the images (below). Please let us know how it goes