How to permanently replace icon?

I'd like to permanently replace my Computer icon with another one, so that the new icon shows up on the taskbar/desktop/start menu/jump menu, instead of the other.

How do I do this? (I know about the Properties>Change Icon thing, but I want to change it for good, so that there's no trace of the original icon on the computer)

Cam said:

... I want to change it for good, so that there's no trace of the original icon on the computer)

Well, you cannot do that, but you can change your icons. I like WinBubble. for this task.

I know this is old but since there is no answer I will explain.

You can do this with a program called resource hacker which can also be used to change much more. For example I use resource hacker to change my splash screen for Photoshop.

*WARNING* Backup your shit before using this if you screw up it's going to break your program. The program does this automatically but it's better to be safe than sorry.

Once you install the software it will add "open using resource hacker" to your context menu.
Once the software is loaded up you will see a list of folders. Expand the folder named icon. "icons will always be 1033"
Right click the icon and select replace resource.
Next click open file with new icon and add your .ICO and save it.

Resource Hacker