I say go the DiY route and buy a replacement touch sensitive overlay. The part itself will run you about 5 bucks before shipping most places, and you'll want a tri-wing screwdriver and a small philips head screwdriver (I use a jewlers screwdriver for that) The repair itself will take about ten minutes, and is very easy to do and fairly idiot-proof. You basically have to take the battery out, and unscrew about 7 tri-wing screws to get the case off, then you disconnect the data ribbons, unscrew the motherboard, and lift it up, then take the touchscreen off, put the new one on, reconnect the data cables, and reassemble it.
If you decide to do this, and your DS starts up and then shuts off instantly, it means the data cables connections are loose, and you need to push them in more, or you damaged them somehow. Don't touch the gold connectors, and don't crimp them and you'll be fine. All this may sound daunting, but once you actually do it you'll fly through it in no time.