I narrowed down the problem to the components in front of the SCART socket housing, and I did go over them with solder, and I also checked for bad joints on the SCART socket itself, but nothing worked!
It's an intermittent fault cured with heat, so the solution is to blow the hairdryer through the side vent which instantly restores the picture, until it cools down and has to be done again!
Unfortunately, during the disassembly, I disfigured the back of the case slightly, and the fan no longer operates. The positive side-effect of this, however, is that it's only necessary now to use the hairdryer once, as the warm air stays inside for the duration of the session!