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That is a 100k, 0402 sized SMT Resistor. It's used as a Pull Down to keep the L3 button line from floating. Floating button lines can do all kinds of weirdo things, so install a new Resistor and then see how the controller acts.
That is an FFC connector, Flat Flex Cable connector. 12 pin, SMT. 0.5mm pitch. Something like the Molex 0781191128 should work if you can find it. https://www.digikey.com/product-detail/en/molex/0781191128/WM20468CT-ND/8638615Also the Kyocera 046244412010846+ should work. - https://www.digikey.com/product-detail/en/kyocera-international-inc-electronic-components/046244412010846/1253-046244412010846-CT-ND/10313426You can skip installing the connector and just wire up the USB lines to make sure it charges and works, just be careful as it is easy to damage those pads. It's kind of rare for a connector to break off like that 'clean' and not tear up at least 1 trace in the process. All you really need to make it work/charge are 5v, D-, D+ and Ground.1 - 5v2 - 5v3 - LED+4 - BLUE-5 - RED-6 - GREEN-7 - GND8 - GND9 - D-10 - D+11 - GND12 - GNDLeft side are even numbers, right side are odd.
Take a Q-tip and some rubbing alcohol to those contacts and that whole area first. The carbon coating (black stuff) has been removed from that last contact there, which is the one for R2, so it may be causing an intermittent connection there making it act up. You can try cutting a small rectangle piece of paper the same size as the foam piece that sits in the plastic piece that holds the button flex board, then install it under the foam piece, so it puts a tad more pressure on the contacts when the controller is together. That exposed copper contact will eventually corrode, so even if cleaning it up and putting a little more pressure on it gets it going again, it's working days are numbered. The best thing to do would be to recoat it, and about your only option there is to use a rear window defogger repair kit. Clean (barely scrape) the copper so it's shiny again, then mask it off and try to paint it the same size and thickness as the other ones. Don't just dump some solder on it, it will just tarnish as well and eventually fail since there is nothing to 'dig' into it when it makes contact with the flex board.
They are the same 3.2v Regulator.
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