im having the same issue.. One day i was using it and literally the next day, it would not power on. When you move the machine, the back lights come on but as soon as you hit the power button, they all go out... Give it a min or two and hit the power button again and you get a flicker around the HDMI port. I suspect the PSU as well. looks like all the caps are good, the large main caps are fluctuating from high to low voltage as expected. Then when you get to the spots you id in your picture, im getting...
1)23V AC
2)23V AC
3)23V AC
4)23V AC
i thought this end would be DC, but testing dc on the multimeter it starts giving me numbers like 0.7mV and bouncing around those and getting really flaky till it gives me the .OL
im no expert but this should indicate a bad PSU. Transformers seem good because its not 110 coming out there so probably bad voltage regulators.
As for a place to put the negative probe, you will want to look for the blue capacitors on the opposite end of your marked probe points. if you look at the board were the mounting screw is (probably need to take it out like i did) on the board next to that mount point is a ground symbol.
Not saying anything i did is right, but just what i found and tested and power supplies are usually the first things that go bad in anything and assuming that is or may be the case here too.
Looks like you posted this a while ago, have you resolved it? What results were you getting in all your testing and observed behaviors?
Thanks and hope this helps!
Edit: also, if i connect my meter between point 1 and point 2, in AC, i get a steady 2.4mV... DC mode, i get 0.7mV. Same thing if i connect 3 and 4 with my probes. Connecting 1 and 4 for example, i get nothing, no responce. I figure the left side of the board is a + and - then the same thing for the right side of the board. Hard to tell which is positive or negative, usually my meter will indicate that, but not in this case. May be another indication of an issue