What you initially describe sounds like an inverter cable being crimped, but I have a question -- when the screen goes out, do you have a faint image, or is it completely black? If you have a faint image, you're looking at a crimped inverter cable, and if it's completely black, most likely your reflow job was not totally effective and you're still dealing with the G3 video issue. When you clamp the laptop just to the left of the trackpad, does that affect whether the video is on or not, or cause artifacts on the screen?
The second part of what you describe sounds like a power issue, although I'm suspicious, again, that you are seeing lingering effects of a bad reflow job. Are you still unable to power it on, even with the battery removed (I would always remove the battery for the purpose of testing)? Is the light on the AC adapter plug solid green when the battery is out? Are you sure the machine isn't just stuck in sleep mode, with a battery that is too weak to power it on again?
It could conceivably be the reed switch forcing your machine into sleep mode (I often just remove the reed switch, in order to tell if that's it), but that in conjunction with the power issue and the fact that it's a video issue machine makes me think you're just suffering from erratic after-effects of a reflow job. There is no 100% perfect way to fix a G3 with the video issue, except by replacing the video chip with the use of a $15K rework station, and most people who do the procedure aren't competent and don't have the proper tools to do it right. And let's face it, a G3 laptop that is work at max $150 today is just not worth what it costs to do it right.