First, make sure the cable is not the problem. Can you try using a different cable or plugging something else in with the cable you were using to see if it works? Make sure there is nothing lodged in the charging port and that the cable is fully inserted.
Looks like there’s a bad connection to the top screen. Could be a loose or damaged cable or just a bad screen. Its worth noting that based on the videos, this is a New 3ds XL, not the older 3ds xl. The relevant repair guide can be found here. If you are comfortable with it and have the tools, you could first try checking where the ribbon cables to make sure they have a good connection. If they do you might be looking at needing a new screen.
I cant quite see the crack in the picture, but if it is on the screen or the casing the answer is likely not as much as it was. It would still be splash resistant and would likely be fine but I wouldn’t recommend submerging it for any length of time, but rain or water splashes probably wont cause you any problems .
you should try defragmenting your hard drive. press windows then type defrag. the program should come up, then run it. you will need to be an admin in order to do this.