Well, replacing the electrolytic capacitor didn't work. This following image shows the old cap. The three following images show the new cap I soldered onto the board. Maybe I did something wrong? I tried soldering it just like the old one was. If I did everything correctly, then the issue lies somewhere else, but I can't find much information about my wii remote model, which seems to be the last one, with motion plus built-in, so I'm pretty much in the dark here. Also, I can't see any corrosion on the metal parts that connect to the batteries, so I just can't explain why this controller would turn on sometimes and sometimes not. Again, if I did everything correctly, then at least this capacitor issue is discarted.
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The next images show the new electrolytic capacitor I soldered. Thanks
@CMDreamer for the help with avoiding accidents and bad stuff. One interesting thing is the new cap barely fit on the board, bc it was just too large compared to the old one. As the first one had the positive lead soldered, from what I could tell, I soldered it. Tried soldering the negative lead, but with no success, but it didn't have any solder originally, so maybe no problem here.
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3300uf 6,3V is the cap I used:
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This is the back side of the board. I soldered the cap leads here:
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