Hello,
I just successfully did a DIY repair on this problem so I thought I would share. The problem is certainly NOT in the video card- that is another issue altogether. It is also not soldering exactly. The electrical connections at the corners of the display are poorly designed. The flat ribbon style wires terminate in plastic plugs that have 5 or 6 contact points that meet surface type (flush wires basically) contacts on the monitor chassis. The plugs are weak and there is not enough positive pressure designed into them to push the 2 sides together. Very poor engineering.
There is a Youtube video of a British gent ripping it all apart and manually soldering these connections. Such is beyond the skill of 99.99% of people. The wires are VERY fine- thinner than common string.
My solution was far easier to execute: I made tiny wedges to push the plastic plug into the surface contacts to encourage a proper connection. I used plastic construction shims that are normally employed installing doors an windows. Traditionally wood, these shims are now common and they have a very fine taper to them that was perfect to this fix. So I cut out ting little wedge blocks just larger (at the wide end) than the gap behind the plastic plugs. Took a couple tries and some sanding but not too difficult if you have a good magnifying glass and common tools. I pushed them into the gaps behind the plug (opposite side from gold contacts that are visible) with needlenose pliers and used a drop of superglue to secure in place. All of the above is under a layer of aluminum tape, clear tape and metal mesh tape that must be pulled and cut away to access the problem area (easy part).
Display is fine now and I'm pretty thrilled to not have to buy a separate monitor. I will note that I am fed-up with Apple failing ot deliver a premium product at thier premium prices. Especially now that RAM is no longer user-upgradable in most models, I have transitioned to using Adobe Photoshop Elements and Google Pics rather than Photos and iCloud. Next time anyone in my family needs an upgrade (we own 4 Macs), it will be a Windows box.