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If the power is staying on, check if you can toggle the caps lock and/or numlock lights on your keyboard if you have them which could indicate the system is getting to the bios at least, but don't expect your system can do that.
Although there are different sizes of adapter tips used, the G20AJ does use similar adapters to some of the ASUS notebooks although the tip is often (but not always) straight rather than at a right-angle to make it easier to unplug which should not be a big deal for this discussion.
Anyway, my information shows the G20AJ 180W adapter has a 5.5mm diameter tip which is similar to many of the older ASUS notebooks, so you can try to find an older notebook adapter with 5.5mm tip although you need to check the wattage too.
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ADAPTER 180W 19.5V 3P(5.5PIH)
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If you're in the U.S., it looks like the U.S. ASUS store is selling the 230W, 19.5V notebook adapter with 5.5 mm diameter tip that you can use as the 180W adapter if you have any interest in trying that even though it is a larger adapter than you need, but should still work fine.
Otherwise, the 180W adapter with 5.5mm tip is not being sold by the U.S. ASUS store, so you may want to look for the 180W version elsewhere.
https://store.asus.com/us/item/202001AM040000006/adapters-ASUS-Adapter-230W-19.5V-3P-%285.5PHI%29-wi...
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Not sure how much time, effort, and money you want to spend on this, but it's not for sure an AC adapter problem, so wondering if you have a shop you trust that you want to ask to check into it more, or maybe it's something you want to consider if another AC adapter does not help.
Also, if you were not aware of it, many of the G20AJ units will use two AC adapters (the 230W adapter used by the G20AJ is not the same one mentioned above as the 180W adapter substitute, so please be aware of this ) rather than just one depending on the video card used, so wondering if you may have been missing an AC adapter as well if you want to check your video card specs, but if it was running fine with just one adapter and you want to get it back to how it was before, you don't need to worry about this part.
Your graphics performance for games will probably suffer if you are missing one of the adapters you are supposed to be using though.
It should not have much to do with the problem you are seeing right now and is only something to look into later if you can get the system working again.
https://www.asus.com/us/support/FAQ/1010575