I am trying to interface two new I2C 20x4 SainSmart to my Arduino Uno and i am having no success.
I have tried connecting the the SDA and SCL with and without pull up resistors (1k & 10k) and in both cases the I2C ID sketch says no I2C devices found and the screens show two horizontal lines.
Additionally, i have run the simple "Blink" sketch with a LED across Pins 4 & 5 to test the outputs and they do indeed work.
It seems pretty clear from the picture that you have the +5v and gnd wires connected but some further checks might be in order.
You refer to pins 4 & 5, tested. Do you mean A4 & A5? These are the pins for the SDA and SCL but are called pins 18 & 19 in the code.
Are you sure you have the right library in installed? The display will not work with the standard LiquidCrystal library that comes with Arduino and, needless to say, the Arduino LCD examples don't work either. You probably need LiquidCrystal_I2C.h, which has its own examples included.