I got a 2DS in to repair that had a similar problem. The only way I was able to fix this was by opening up the system and reseating the slider as the pin popped out of place. Since you have the tools, you'll want to take it slow and get in there gently. I advise a '''high amount of caution''' here as you can easily tear the camera ribbon here. I tore the camera ribbon on my 2nd entry into the housing so be careful going in.
You may also need to solder the sleep slider back to the board as well. My 2DS has the right side lifted from the damage caused by the previous owner.
Good luck and be patient in this fix.
P.S. - Due to the age of this post, if you've already fix it, please post back so we can hear what you did to fix this.