How to display Trash and Home folder icons?

You can enable them using Unsettings:

Or you can use the command line:

gsettings set org.gnome.nautilus.desktop home-icon-visible true
gsettings set org.gnome.nautilus.desktop computer-icon-visible true
gsettings set org.gnome.nautilus.desktop trash-icon-visible true
gsettings set org.gnome.nautilus.desktop network-icon-visible true

Story behind

I don't have any of those icons in my desktop, so I just checked the options that you mentioned and this were already activated!

So, maybe there is a problem with dconf, well I don't know, but these configurations doesn't make any change in my system (Ubuntu 12.10).

The answer

1. Install Ubuntu Tweak

2. Click in the Tweaks label and then in the Desktop Icons icon (sounds recursive :) )

   

3. Finally you should see a window similar than the following allowing you to show/hide the icons.

   

This is my result. It works even when donf have different values.