Those are ranges, you want to pick the one that comes after your target voltage. For example, if you are measuring something that is supposed to be 1.2V, you set it to 2V for the most accurate results. If something is supposed to be 5V, or 12V, you need to set it to 20V. Setting it below or above that will produce less accurate or extremely wrong results.
Also you need to know which pins are which, before you can really make judgements as to whether it is "dead". For instance, in the first link I gave you, he shows which pins are supposed to be what, and tells you what to test. The results you posted don't really make sense to me, because I don't know which pins you're testing. 5.1 volts would be perfectly acceptable for SOME pins on the 20-pin ATX motherboard connector. Like the 5V rails. But not acceptable for 12V.
There are other problems with this kind of basic testing, like for example this doesn't show results of the PSU with any sort of load at all. Plus your fan isn't spinning up, which means you either need to replace the fan (something I've not done on a PSU myself) or get a new PSU. But the point I was trying to make in my previous post was that even if you have a new working PSU, there may be something else wrong. So you can test away with your multimeter and that first guide, but you still need to borrow/buy a working PSU in order to figure out if something else is broken. Like the power switch.
That reminds me, if you didn't get what I was saying with the screwdriver thing: The power switch normally connects to two pins towards the front of your motherboard. But his switch went bad, so temporarily he removed the "Power SW" wires from his board and connected those two pins together with a screwdriver head. A wire would work too, but be careful to avoid connecting other pins together.
Edit: I also would need you to measure your PSU and how much extra space there is if you had to put a larger unit in there. I can't clearly see from these pictures if that is ATX-sized.