"Buttons on Nintendo 2DS get stuck?"に関する回答The 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.
"Why isn't my touchscreen working?"に関する回答There 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.
"Why won't my Nintendo 2DS power on?"に関する回答It would be helpful to know more about your problem, but for general reference this troubleshooting guide has some information on your problem.