If it doesn't work (why the hell wouldn't it work?!), then you could format your system without SDCard inserted, but you would need to manually delete the no longer usable data folder in your Nintendo 3DS folder to free up some space.
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WAIT!
Boot your current NAND without SDCard inserted, and please post the list of apps you see! This is needed to identify some incompatible apps that could cause the softbrick.
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WAIT!
Boot your current NAND without SDCard inserted, and please post the list of apps you see! This is needed to identify some incompatible apps that could cause the softbrick.