the white goo is almost always hot melt glue, they use that on larger parts to hold them in place while going down the line (or a tinfoil hat theory that over time has become a fact is that it "provides more stability against mechanical shock", eventhough you can pick the crap off with no effort and your finger )

the other thing you describe is most likely an inductor that has been plastic dipped and is quite common in apple power supplies (pc power supplies usually dont dip theirs cause it really is not necessary in most cases, and usually they use doughnut cores, where as apple liked those cylinder ones for whatever reasons)

the best way to check a power supply is looking at its voltages with a meter while its under load (ie computer attached and running)