There actually is a way to test the power supply, but for what I've heard, the testing equipment would cost about 50 000, yes, fifty thousand... There may be other methods, too, using oscilloscopes and such, but not everyone has access to those, nor the skills needed to use them. And you've read correctly about he cheap testers. Since they provide no load, even a failing PSU may be able to produce good values. And yes, the yellow goo is factory applied stuff.
The easiest and cheapest way is to use a known good PSU to see if the problems reappear. In your case the testing shouldn't even take long.