Hi
I bough a Lexmark S405 printer with Wifi.
I have a desktop computer using XP, which is connected directly (USB) to the modem.
The modem also have a cable to the router, which is how the router gets internet.
The printer is connected to the router using Wifi (only).
All the rest of the computers are connected to the router by Wifi.
I wanted to know if I'm supposed to be able to install my printer by typing its IP , even when the configuration of the cables are like I mentioned.

If a printer is WiFi and its configured to connect to your router then any PC on the network can print to it. Only the printer and the PC you are using needs to be powered up.

Generally you can add the printer as a Network printer.

But my computer is not "taking the internet" from the router, so its actually not in the same network. And I actually can't ping my printer..

Does the printer support an Internet connection? Most printers don't. Any device on the router should be on the same network!

It has wifi.
My desktop is not on the same network , because its plugged directly to the modem and not to the router (thats why it has its own IP address)
Any soloution for this except of plug my computer to the router?

First, please don't use the comments feature Use the Answer options.

Why isn't your PC connect to the router? That's the best way.