Pretty easy solution actually, replace the MyComputer icon with a blank icon, and rename it to nothing. Move it somewhere out of the way before you do this and you will never know it's there.
(You need a blank icon first to replace it with, make one yourself with iconedit or similar).
To "hide" and not disable the functionality of either, do the following regedits (don't add the ##'s those are either 1,2,3 etc depending on which icon inside your icon file you wish to use).
Network Neighborhood:
Open HKEY_CLASSES_ROOT\ CLSID\ {208D2C60-3AEA-1069-A2D7-08002B30309D}\ DefaultIcon, and change the (Default) value to "filename, ##."
My Computer:
Open HKEY_CLASSES_ROOT\ CLSID\ {20D04FE0-3AEA-1069-A2D8-08002B30309D}\ DefaultIcon, and change the (Default) value to "filename, ##."
Edit: Ah, actually, here's even better instructions and details :-)
http://www.annoyances.org/exec/show/article02-016
