crwdns2890332:0Buttons on Nintendo 2DS get stuck?crwdne2890332:0The trigger buttons are supported by springs, so it's possible that those have broken or somehow come out. Its also possible that something sticky might have gotten under the button and is holding it down. This Guide links to some repair documents that you might find useful.
crwdns2890332:0Why isn't my touchscreen working?crwdne2890332:0There could be several causes for the touch screen not responding to being touched. Here Is a troubleshooting guide that explores a couple possible causes and solutions.
crwdns2890332:0Why won't my Nintendo 2DS power on?crwdne2890332:0It would be helpful to know more about your problem, but for general reference this troubleshooting guide has some information on your problem.