Can it still be repaired?

DIO  first stop trying to charge it or trying to turn it on. As a matter of fact remove the battery. discard it properly. After that you will need to complete disassemble your 2DSXL. Use these guides New Nintendo 2DS XL for that.

Take a careful and close look at all components and connectors. Truly assess the damage. Look for major corrosion, evaluate the pins in the connectors etc,. Take a look at all connectors as well as cable ends. You will have to remove all the EMI shields. If you do not remove the shields, you are not cleaning the board. Once you got the gross contamination cleaned, use 90%+ isopropyl alcohol and clean your parts some more. For a proper cleaning, use this guide. It was written for an Apple iPhone 3G but it is still pertinent to handheld device as well. I can not stress the importance of a good cleaning enough, so do it over and over while replacing the alcohol after each cleaning. Do not use compressed air for the cleaning since that can drive liquid as well as corrosion particles into areas that will cause trouble later on. Also, you do not need to leave it to dry for a day. Isopropyl alcohol in the higher concentration will evaporate quickly and dissipate the water. The importance here is the cleaning. It would of course be best to get it professionally cleaned via ultrasonic cleaning but this will at least get you in the vicinity. Do not forget to replace the battery. This is a must and not an option. It will fail if you do not take care of it now. After that, reassemble your Nintendo and re-evaluate.

Of course you can always post some GOOD pictures with your QUESTION if you are getting stuck somewhere with this process. iFixitでの質問に画像を追加する方法