Resolder all pins of the flyback transformer, and HOT for good measure. Also any other inductors you can find on the mobo - in the PSU, the smaller transformers driving the output transistors, any linearity compensation coils for the yoke.

This should stop the tearing, but lack of pincusion correction this bad is most likely a very degraded or pretty much dry electrolytic cap. Anything close to heat source or flyback needs to go if you have no way of testing them. I'd recap the PSU as well. Everything else might be a good idea too - they don't all go bad usually but again if you have no way to test then just replace. With good quality caps, preferably 105C for the cricital areas like PSU and flyback.

The longer you try to run this monitor with these problems, the higher the chances of some major failure like HOT shorting and taking out flyback and/or control chip with it.