Hm, I’m new too, so I can share your frustration 
but I’m not sure I can help. I am running with BBBlue at the moment, which is as near to BBBlack as you can get, but I have not experienced any of the problems you describe.
I’ve already flashed scores of images with Balena, including the latest Buster, Bullseye and Bookworm and the latest Ubuntu 22.04. If I run them without the flasher enabled, they just boot up off the SD card (yes, rootfs is all you need) and if the flasher line is enabled (uncommented) they install on the emmc. I used a 16Gb card - good luck finding a 4gb these days - but that also seems to have the advantage that you get the extra memory to work with if you choose not to flash. Any work you do is preserved into the next boot, of course.
I am trying to think what your problem could be. A bad flash? A bad SD card? I am assuming you are using one of the latest provided images. Are you certain you are using the correct one for a 335 chip? I.e. not a 57x one? It sounds like it’s trying to boot; all the blue lights on signifies the start of the booting process as far as I can tell.
Use image from here: Latest Software Images - BeagleBoard
Incidentally, you should be able to SSH to the original installation via the usb cable and 192.168.7.2.
If you can’t there may be something wrong with the board. Once you’re in you can set the proper WiFi up with connmanctl and operate as normal (w/o usb cable)
Also, if you flash Bullseye then connmanctl has been replaced by wpa_cli or if you use Bookworm or Ubuntu by iwctl! These changes are not documented, you have to search this board, the answer is always there somewhere - just not too obvious - so I hope this helps.
PS. Ah, yes, also be aware that the latest of the old Buster 10.3 release Debian 10.x (Buster) - Monthly Snapshot - 2023-07-01 - (FINAL) may still be best if you need access to the PWM, there seem to be some irregularities in the configuration of the device tree that messes up access in Debian 11 & 12, I’m still exploring that so I don’t want to say the wrong thing, hopefully it won’t be too hard to fix.