HansDampft has it figured out. So like all of you I had an APE-1264 from ebay that was not acting right. Stuck in a boot loop when plugged in. Would flash green, then solid amber for a while, then off for a moment, flash green once, then back to solid amber. From reading around, it sounded like it was never getting out of its boot cycle. Some forums had some witchdoctor solutions "plug, unplug, 5 mins press reset button, eat salted fish, take a big dump, plug it in again and it will work" kind of stuff. Tried a few but no luck, finally read Hans and a few others saying that they cracked theirs open (no mean feat), but were able to fix it by simply unplugging/replugging a little cable that connected the two halves together. So iFixit has a tutorial on how to get it open, which looks pretty **** hairy (https://www.ifixit.com/Guide/Apple+AirPort+Express+Base+Station+Power+Supply+Kit /7090). I decided that a dremel isn't a good plastic cutting tool, and that I was going to cut it open with a plastic pipe cutting tool, pictured in image 1.
Was a beast, but I was able to cut the thing open with minimal damage to the case. I went around a few times, starting from the power plug area, and cutting deeper with each pass. You only need to cut on the following faces: The face next to the power plug without the sticker (as shown in the pic) and the face that has the led light. The side with the ports isn't glued, and the side with the sticker can act as a hinge if you cut the other two sides well. Eventually I was able to pry it open, not sure of the original state of the cable, because the opening was somewhat sudden.

I plugged the little cable back in after letting it sit for a few mins and then stuck it into the power strip. I felt pretty hardcore running my APE with the top down and chrome spinning.

At first I thought it was BS, because it did the same thing, but after a min, it started flashing yellow, and I was able to log in and configure it as usual. A bit of packing tape and its good as new(ish).

Anyway, a decent little fix 🙂