Thank you very much for your help, now i think i figured out my problem. considering the 74HC595 of course i believe you, i was just a bit confused because there are loads of tutorials out there which say this IC would just be right (one of them is from arduino personally ;))
So there is just one (as we say in switzerland) snarl in my head: at all times theres just one row high, the others are low. this makes sense to me. so if i want to light up the first 4 LEDs ind the first row(forget about the power problems) i set the first 4 colums to low. but this implies that the other columns are set to high (or is this wrong?). so at this specific led (the second 4) there are 5V at both the anode and the cathode. and for the other rows this means that the power "flows" from the column pins (since they're high) to the row pins which are low. i guess theres a huge mistake but i dont see it.
thank you again!