Let me preface this by saying I ***''hate''*** working on 3DS devices. It is the worst! Especially and above all else the New Nintendo 3DS XL![br]
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That being said, the behavior you're experiencing is commonly reported online as one of those ribbon cables, but that's largely a misconception. That pop is from the power management, and it will occur if ''any'' major component isn't managing power properly. This can be caused if it is not plugged in properly, but also if it is the wrong component all together.[br]
For one example, are you aware that Nintendo 3DS XL screens and Nintendo New 3DS XL screens are the exact same physical dimensions, and you can put one in the other's console? In fact, the only difference visible at all is one of the two ribbon cables that plugs into the 3D switch board has 6 pins instead of 4. That's it. The only difference. It simply will not work when plugged in, however, and you will get that "pop" and failure every time.
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I can see from your photo that you disassembled this in the "pop out the hinge and remove the entire top assembly" method instead of the "try and roll the cables and stuff them through the hole" method that is recommended on the official iFixit guide, which is good. Most of the damaged cables I see are from people trying to do it the iFixit way instead of the objectively superior remove the top shell way (iFixit should really change their guide, but I digress). [br]
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If you've inspected all of those cables and they are all good, I would carefully put it all back together. Then double check the home button cable and/or anything else you touched while you were in it this time. Try putting back the old home button cable and see if it works. I don't know that specific ribbon cable off the top of my head but I suppose it is visually identical or close to it to be the wrong cable that just looks the same.