Hmm it depends. The switch can break easily with enough force. Alright when you turn it on, does it show anything on the screen at all? If no, and if you're switch feels a bit ligther to press, or doesn't have that spring effect, then yeah, the switch is broken, but it ain't too hard to repair. There are 2 ways to fix it:
1. Get a new ds power switch, and remove the other one. It's kinda hard to repair mainly due to the 4 points in the switch to have to desolder, one by one, with as little force as possible, because I remember ripping a trace out and I had to rewire one of those little pins T_T.
2. This is much easier, just ignore the switch, or remove the switch, and get a momemtary switch (like one of those very small button switches, here's a picture)
If the switch has 4 pin, then find the 2 pins that are opposite to each other. If it's 2, then perfect, just wire one pin to PWSW and the other to one of the 3 pins on the switch or any ground you have on the DS. If you push it, and it works, then good job
. If not, then take a few steps back and check anything that might have gone wrong (i.e.- Cold soldering point, wrong wiring)
Hopefully it's only the switch that;s the problem. If one of the screen flashes, then one of the screens are busted.