Your title and post are contradictory. Is the problem that the 3DS won't boot without the SD card, or is the problem that the 3DS won't boot with the SD card?
If it's the former, you need to put the Luma3DS boot.firm onto the CTRNAND root.
When you hold Select while booting the 3DS with and without the SD card, which version of Luma3DS is displayed?