Did you try to boot the BBB without the cape? The instructions for booting with an SD card remind you,
If you are using your Beagle with an SD (microSD) card, make sure it is inserted ahead of providing power. Most Beagles include programmed on-board flash and therefore do not require an SD card to be inserted.
I bet you already did this step, so see how the BBB works without the cape.
If it still fails without the cape, but boots from the eMMC as you mentioned, maybe the card isn't built correctly? (Debian not copied into SD card properly).
Maybe you can take a video of the failure and I'll compare it to my BBB to help.