I used NiLuJe's jailbreak and usbnetwork packages here:
I use kindle-usbnetwork-0.37.N.zip on all of my Kindle 3s.
Be sure to use the correct update*.bin file inside that zip file. For 3.3 firmware, you need to use update_jailbreak_0.10.N_k3g-3.2.1_install.bin
Be sure it has 3.2.1 in the filename.
ERROR CODE 3 means you probably used one of the other K3 versions.
Also, I recommend adding an AUTO file inside the usbnet folder, so it boots up with usbnet active. You can use scp or WinSCP to copy files to it when in SSH mode. Or delete the AUTO file to use USB drive mode.
You can also activate usbnet with search commands, but that would be difficult with a broken screen.
Try installing the usbnet file in your zip file, with 3.2.1 in the name. It works for me.
I have multiple K3s (wifi-only, and 3G) and they have different menu items grayed out, so it can be difficult to "blind-navigate" the menus.
I found that activating voice guide makes a kindle with a broken display MUCH more usable. I borrowed a display from a good K3 to get voice guide activated successfully though.
EDIT: Please post whether using the "3.2.1" version worked for you.