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I have a Late 2010 11-inch MacBook Air that my aunt gave me to repair and I am having difficulty seeing if it will boot up or not. I found out that the battery has swollen in the machine so I had threw it out to prevent a fire or explosion. After that, I plugged in the machine to see if it would boot then but it still won’t. I tried resetting the SMC and also pressing down the power button, then plugging in the power adapter, still holding down the power button. Nothing worked. Is there something wrong with the logic board or I/O board? After plugging in my 85 watt power adapter, it just shows a green light continuously. Sometimes it will show a dim green light. Please help, thanks Here are picture of the boards

First a 85Watt unit is too much for your system you need a 45W MagSafe 2 Power Adapter for MacBook Air. It also sounds like you have a deeper issue with either the MacBook Air 11" (Late 2010) I/O Board or within the charging logic in the main logic board. For now lets get a good set of pictures of the I/O board so we can check the contacts and look for corrosion Adding images to an existing question. Follow this guide MacBook Air 11" Late 2010 I/O Board Replacement

Well this video might help you in fixing: Macbook Air 13 2012-2017 , Will start without battery but wont start with it