I had a similar issue with my Picasso II some years ago, a rolling display with lines. I couldn't get in to any of the screen modes. I replaced all the caps on the board and replaced the burnt resister with a larger 1/2 watt resistor of the same value to prevent the same failure ( a common failure in these cards ) but it made no difference.
The fix was replacing the power supply in my A3000. It might be a good idea to check your PSU voltages under load to see if there's a problem there. There are two relays in the Picasso II and you should be able to hear them pulse as you activate one of the screen modes.
