If you are uncomfortable with rooting, then you may not wish to proceed, but these steps make minimal modifications and are what I used to remove the DDDRRRROIIIID sound (as well as the camera click sound) and then return the phone to an unrooted state.
1. I downloaded Z4root on my PC, then moved it to the SD Card over the USB cable. After installing and rooting using Z4root, I looked for the "Root Explorer" app that people refer to, but all I found was a paid app that I didn't feel like paying for.
2. Since I am quite comfortable with Linux, instead of "Root Explorer", I used "Android Terminal Emulator" (you can find it on the Android Market) and performed the following commands in order to rename the two files (droid.ogg and camera_click.ogg).
Code:
su
mount -o remount,rw -t ext3 /dev/block/mmcblk1p21 /system
cd /system/media
mv droid.ogg droid.orig
cd /system/media/audio/ui
mv camera_click.ogg camera_click.orig
mount -o ro,remount -t ext3 /dev/block/mmcblk1p21 /system
sync
reboot
The boot DDDRROIIIDDD sound and the camera click sounds are now both gone.
3. I then went back into Z4root and unrooted. So far so good.