i don't need to see a photo,i worked on hundreds of these monitor type
start be locating the sync wire,you will see a green plug with 5 or 6 wires coloured red/green/blue/black/white and possibly yellow
the white and yellow are sync wires,try wiggling the wire at the plug of the inverter board and the main chassis video plug to see if it affects the picture
as for bad solder joints you would need to have experience to know what you're looking for,don't attempt this if you are not familiar with monitors as you could get a nasty shock or damage the chassis-get a pro in