Can you provide more information like whether the wireless interface get recognized or not?can see other access points in your area ? also post the result of following command " ifconfig && lshw | grep wire "
I downloaded Debian Buster a week or so back to use live on usb with persistence ; Debian is community driven with ethos for free software. I noted there is an iso missing wifi drivers and another one called "with none free" i.e it has the wifi drivers. Do you remember which one you downloaded. With an ethernet connection solution ( i'm guessing since wifi and power flaky here so no time to look at image) will be to enable none free repo in your mirror list
If you want to install any non-free package maintained by Debian, you need to enable contrib and non-free repositories. To do so, open /etc/apt/sources.list with a text editor, and append "contrib non-free" to each source.
The following is an example of /etc/apt/sources.list for Debian 10 "buster" Release.