How to delete files from my indestructable memory card?

Ultimately I replaced the card, and everything is now working. Multiple attempts to delete the files via different systems all failed. After more research it appears that some SD cards/flash memory are capable of changing a failed portion of the card to read-only, which allows the writable portion to still accept changes while not allowing any of the old items to be changed. Since the device was already full, it is pretty much useless as anything more than a permanent backup. Thanks for everyone's advice.

I'll suggest you try a GNU/Linux box (a live CD should do) andshred all the files. Look for errors in kernel.log and dmesg when you do - if the device mounts read-only, the FS is corrupted, reparition it.