LCD works, but some pixel lines don't

I'm desperately trying to get my small 16x2 character LCD to work (SD1602H), so far I hooked it up to a power source and got it to blacken the pixels a bit.

I don't have a potentiometer to regulate the contrast, so I use a 10K resistor and see a very small difference, but a difference nevertheless, so it's working.

The problem is that some of the pixel lines of the upper character line do not, for the lack of a better word, "blacken" when I turn it on.

When I push down on the data lines (the small lines on the upper part of the screen) the pixel lines start working again, but as soon as I release them the pixels stop working again, so garbage or usable?

I've had the same problem on my calculator and some other devices using a similar display, I really hope it fixable.