I've had a similar experience with a normal DSi. In my case, the app I was using had crashed, rendering pretty much all means of device input useless. Even the power button did not work at first, but a few minutes later, it successfully powered down.
The above solution should work in most cases, provided that you wait a few minutes and reboot.
If that fails, turn your backlight and sound up to the max, leave the system open, and wait for the battery to die.
There's also always the method of just crashing the system by removing the battery, but it obviously can involve electrical shock.
But anyway, what were you using when it went haywire? i.e. cartridge, browser, shop, other app, menu