For starters, that adaptor has the wrong polarity. You're lucky if you havent fried already your AES and your multi. DON'T Use it again.
Also, that adapter that you bought is providing 0.5 Amps which is not enough.
Make sure that the adapter that you bought corresponds to the one that your console needs (9V or 5V).
As I said, don't use any PSU again until you are confident that your console is working and has the right adapter. I recommend you buying from here: https://en.retrogamesupply.com/collections/neo-geo/products/power-supply-for-snk-neo-geo-aes
Also, that adapter that you bought is providing 0.5 Amps which is not enough.
Make sure that the adapter that you bought corresponds to the one that your console needs (9V or 5V).
As I said, don't use any PSU again until you are confident that your console is working and has the right adapter. I recommend you buying from here: https://en.retrogamesupply.com/collections/neo-geo/products/power-supply-for-snk-neo-geo-aes