Just received a Picasso II last week for my A2000, and oddly my system does the EXACT same thing.
The more I access the HD or large folder the more horizontal lines I get, making something full screen or dragging windows around can help clean it up, but they eventually start up again.
The mouse also will turn into a large square of garbage.
Hoping your incident will be the same with me, ordered an ATX power supply adapter as I have an extra ATX power supply around to test it with.
I know this is an ancient thread, but did replacing the power supply last?
I had exactly the same problem WITHOUT a Picasso II. It happened when i replaced the 2.0 Kickstart with a 3.1.
Turned out to be a faulty Agnus :-O ... I replaced Agnus and no more horizontal lines and garbage on the mouse pointer.
