I did not find it necessary to detach this cable. The battery slid out from under it easily.
The “two plastic mounts” are not “snap buttons.” There are two nuts mounted on the back panel, and they are attached by screws from the front. The process described in this comment will at least separate the nuts from the back panel. The back panel itself may crack, or even the nut and its attachment may remain connected to screw and a hole be formed in the back panel.
The proper procedure is to remove the display as shown here. Then remove the black screws connecting to the back panel, instead of all the silver screws in step 5. Then use an opening tool on the back panel and remove it safely to access the battery from the back side.
Unfortunately it’s hard to find the adhesive cutout needed to properly re-attach the display after removal (I only found the part GH81-13867A on eBay from Europe, about $28 with shipping). And even then it would be hard to remove the old adhesive well. We’ll likely have to reply on reuse of the old adhesive, and the display will not longer be attached perfectly as before.
One way to easily access the bracket (for removal and for insertion) is to rotate the display around the cable connection horizontally, so that the screen is not above the bracket but rather to the side.
When disassembling, note that the screen assembly is hinged to the bottom on the edge away from the home button. After first opening the screen to about 30 degrees as above, slide the screen in the direction where the home button was to disengage this hinge (this is the first bullet item in step 13 below). Then rotate to expose the bracket to eyes and tweezers.
jor_rox - If you plug power again, does the charging screen show again? If so, the main board is still alive.
First to suspect is the button cable. Be sure all the cables are well seated.
To Damon - possibly the thread on the bottom of the upper case is obstructed.
I found that I needed to fight the latch magnet with the right-most screw in the photo. The screw was pulled away from the hole so a magnetized screwdriver was not enough to place it. I needed tweezers to hold the screw in place until it bit.
My battery arrived without replacement adhesive and I just placed it in the middle housing. A bit of adhesive remained to help is stay in place while I put the middle housing and the front assembly together. There is a channel in the middle housing for the battery cable. Be sure to flatten the cable and align it to the housing so that it is oriented correctly to its connector.
I recommend verifying the alignment after replacing only a few screws, and replacing all the connectors. Then turn the phone on and verify that the battery is charging, the buttons work, WiFi and Cellular connections succeed. Only then replace the rest of the screws, the logo and the back.
I chose to separate the cable attached to small connector board. That's by lifting the tape, then lifting the clamp (clear plastic on mine) and pulling the cable straight back. That gave me a bit more room to poke at the connector board from multiple edges to loosen the adhesive.
Replacing the battery connector cover (the second one in the sequence) was tight. I succeeded by first inserting the top left corner (oriented as shown in the picture) into place.
When I tried to lift the battery connector (the second one in the sequence), the plastic lip by which to lift broke off the connector on the battery lead.
I ended up leaving the connector in place and separating the middle housing carefully with the cable still attached. Then, when I could get to the connector from all side, lifting the connector from the cable attachment side.
This comment is about the re-assembly, the inverse of this step:
When pushing the assembly back into the casing, note that there is a spongy block at the bottom of the assembly on the battery/drive side (can be seen on the picture attached to step 12, at the extreme left of the picture). This block scrapes against the casing wall and pushes the circuit board towards the click wheel.
I used a spudger to gently push the circuit board away from the click wheel and compress this block. This allows the assembly to slide into the casing without halting at, or scraping against, the click wheel.