(Sorry for my English, I'm not a native speaker. If you want you can correct my errors, it really helps me.)
Me too. I opened it to try to fix the cameras, and ended with my DSi not turning on. I think it's not necessarely due to a dead battery (for me it's not, my battery works), but it can be something connected to the battery. It can be the charging port or the power board (in my case I think it's the power board that is faulty). You'll have to check with a multimeter to know what isn't working (see online what you need to check).
(By the way, if there are French here that know a good website for Nintendo DSi parts, let me know.)