when fault finding problems there is one thing above all that is needed,logic.
the fact you have a picture is a start
have you done anything to this cab that may have caused this problem?
have you adjusted any of the monitor controls or unplugged anything at any time?
if you have changed anything or moved anything then go back and double check everything you have done first
next try checking the colour and contrast controls on the monitor remote board
check you +5volts to the logic board
golden tee 2005 have a graphics card,check the connections
does another game board show colours?