I am also guessing a dry solder joint on the RGB port, but it might also be other things like the custom chipset. Problem with the A600 is everything is surface mounted so is hard to replace or fix anything. Although replacement motherboards can be found cheap if it turns out to be the problem.

One thing to check is to connect the A600 to a TV using the yellow composite video output on the back. If the picture is still blue then it must be an issue with the hardware itself. If the picture looks in colour and OK then it is probably a problem with the RGB port.