There's a chance you damaged one of the ribbon cables, a few of them (including the upper screen cable) will cause this behavior if damaged. Inspect them closely for any damage, even a tiny fracture could be enough.I have a New 3DS XL (2015 model) with Luma3DS CFW installed onto a 64gb SD card that I changed the broken lower LCD on. The console was working perfectly fine with the broken screen, but after changing the screen the blue power LED comes on for a few seconds then turns itself off. I have checked the resistors to make sure they are all ok and I've unplugged and reinserted every ribbon cable in the 3DS but nothing has changed, the console still won't boot. I've looked through many threads on GBATemp but nothing I have found has helped solve the problem.
Is there anything that I could try to get at least a backup of the entire system so that I can restore it to a new system if I have to buy a new console? or is there anything i can do to get the console fully working again?
EDIT: Just tried the broken screen and the bottom of the screen quickly flashes when the console turns off, if that's of any use to anyone
If it is a damaged ribbon cable then you might need to replace the entire component as a lot of the ribbon cables are soldered onto the component.