I have a Logitech G15 keyboard. It has media controls (like many other KB's) and they work in all the other games I play.

For some hellish reason, the volume and mute buttons do not work with Far Cry (I have 1.4 but it didn;t work with any version). Far Cry also doesn't let me Alt+Tab my way to the desktop - so everytime I want to change the volume, I have to quit the game and do it (LAME!!!!!).

How can I fix this?

Cant help with why the volume control doesnt work, other than its likely to be because you are running the game full screened and as you have seen, Far Cry doesnt like application switching in that mode.

A way around it is to briefly switch to windowed mode.

When in game, open the console using the top left keyboard key under the ESC key.

Type the text inside the quotes "\r_fullscreen 0"

Press return.
You should now be in windowed mode and be able to ALT TAB

To get back to the full screen mode type "\r_fullscreen 1" in the console.

Hope that helps.

I entered the command that you gave me at the menu screen and nothing changed. I still couldn't change volume (there was no window'd mode). Do I need to change my Far Cry Shortcut line to allow for developer tools?

No you dont need any shortcut extension.
Are you sure you entered the command correctly?
ie only the text inside the quotes and not including the quotes themseleves?

The other way to achieve the same effect is to select:
Options
Video
Uncheck Full Screen
Apply

Obviously to alt tab, you need to have another program running.