My ps2 does not respond to the control buttons, but shows a picture on the screen

I can think of two problems here.
First, (not trying to insult your intelligence here) make sure the controller is plugged in all the way. If that doesnt help, the controller may be malfunctioning or the controller port inside the console may be malfunctioning (possibly a loose ribbon cable).
Try the controller in both controller ports and if that doesnt work, try a different controller. If that still doesnt resolve your problem, you may need to fix the controller port.
If you feel comfortable opening the console (keep in mind this would void any warranty you might have and could lead to further damage to the console), you might have a look to see if the ribbon cable to the controller port is loose and/or replace the controller port.