<mod>I deleted a couple of overly snarky posts. Let's keep it civil and friendly, please.</mod>
cblaisd, if the screen is totally kaput and a computer running iTunes doesn't recognize that the iPad is plugged in when you plug it in via USB, then my last-ditch suggestion is to try to put the iPad in DFU mode (Google it) and see if you can get iTunes to recognize it that way.
If not, just bring it to Apple and they'll recycle it. Unless you have the nuclear launch codes on there, nobody is going to try to pull the flash memory out and try to connect it to something that could potentially read it. Destroying the iPad will only make it non-recyclable. If you're feeling extra paranoid, change your passwords for any accounts that were connected to that iPad.
By the way, all: erasing an iOS device doesn't wipe all the flash memory. It just wipes the memory where the hardware encryption key is stored, rendering any data saved on the iPad inaccessible. So, cblaisd- your data stored on your iPad is encrypted anyway. Getting into how one might somehow remove the flash memory, put it into some device (what device?) that could read it and the encryption key, and run iOS enough to harvest data from it, is silly because it assumes there's someone out there motivated enough to steal your iPad from the Apple store (or pose as an employee who receives your iPad). Which I'd be willing to bet serious money there isn't.
If there is such a nefarious plot afoot, then you have bigger things to worry about.