Don't give up. Mine flickered and it turned out to be my ffc connecter. (I had to make an extender and the first one just wasn't quite right.) From your account, you either have a cable or vga or grounding problem. I don't know how your projector is set up. On mine, I have independent control of the lamp and the LCD. This allows me to turn on the LCD and not get blasted by the light and heat. I removed my lamp assembly and I bought a reflector for general utility work and put a 9 watt flouresent bulb in it. That allows me to see the LCD working. Before trying anything here please read the whole post, especially the last part.
Now it is time to start troubleshooting. First question: are all the different parts of your monitor grounded together? Mine had two boards that were well grounded by the chassis they were mounted on. I had to cut the chassis to make things fit in my box. I had to ground the two chassis parts together for reliable operation. This was even though the boards were grounded by cables connecting them. I don't know why they didn't work reliably, perhaps a ground loop of some kind. I don't think this is your problem but I wanted to throw it out there just in case.
From your description, I don't think the ffc cables are the problem either?
That points at your vga input. Take a close look at the vga connector on the lcd monitor control board. Do any of the solder joints look dull or grainy? Touch them up with your soldering iron (with a very small amount of solder). If you're afraid to do that get a friend with lots of soldering experience to do it for you. If everything looks good there, take a look at the vga connector ends (both the make and the female sides, are any of the connection pins smashed, pushed aside or pushed in? If they are, replace the bad connector. From your description of just touching the vga cable making it work and then letting it go and everything going crazy, I would say one(or more) of your wires inside the cable at the connector has broken and is now making intermittent contact. Have you tried replacing the vga cable?
Hope this helps and provides some more ideas. One last thought, the vga cable isn't so stressed that it is being pulled loose from the connector and thus making intermittent contact is it? Maybe it started out fine, but no strain relief was put on it and over time it became stressed. Bye again.
Still waiting for my final parts.