The console screen is warning you that your VCA thumbwheel settings are conflicting so I can't see that would explain your problem with the RGB display... Showcase's power supply comment is a good starting point if you have a multimeter handy to check the voltage rails, they are silkscreen printed on the motherboard if you lower the front panel to the computer. Dan could also be right about synchronisation, I don't know the Dramastic converter but any LCD TV with a scart socket should handle 50Hz RGB if you want to try an alternative display.
My feeling is that the fault may be related the Hi-Res Graphics (HRG card) in the five card TR computer sandwich. If I understand correctly, (and feel free to chip in if I am wrong:-) ) The 82e89 card provides an interface between the SSL computer and the Research Machines Z80 CPU card, this CPU card drives a Research Machines VDU40 40x24 character display and a Research Machines HRG card (320x192 pixels in colour!!) The Research Machines design allows the bottom lines of the picture to come from the VDU40 - this is the stable text box you see on your screen, the upper part of the picture should be the familiar colour graphic image of knobs and switches that is generated by the HRG card.
The fact that you can see the text suggests that the SSL computer can successfully talk to the Z80 card and that the Z80 to VDU40 link is fine. If Showcase and Dan's suggestions don't fix the problem, you might try re-seating the ribbon cables going to the HRG card. If the display eventually stabilises after a few hours then it could be a thermal problem such as a dry-joint or suspect component, a few squirts of freezer spray around the HRG card would be my hunch, but you know how wildly off hunches can be :-)
