Thank you for your answer.
I am using a 19" LCD screen.
I have the problem with gpm even before I start X server. (with gmp, I can only move the cursor up/down. When I old the right click button and move the mouse, the cursor slowly move to the right of the screen, that's really odd). Sometimes, the up/down only bug is happening in KDE too. From my tests, I think it happens in KDE only when I move the mouse in the console before starting X.
The only way I have found to not have this problem is to use one receiver for the keyboard and grab an older wireless mouse and use a second receiver, that way, I can use a wireless keyboard and wireless mouse at the same time.
I have tried tweaking the X11 config file with no good result at all
It really gives me the impression that I have to make a click to "start" a communication between the mouse and receiver.
Also, I forgot to specify but when I click, I can move the cursor for up to 3 seconds, then it stops moving and I have to click once again to make it move.
Thank you for your time!