Good progress thus far.
The IC you found looks bad... but it's hard to say that's the culprit.
Electronics have a tendency to show failure on a more sensitive component than to show it on the actual culprit.
Initial tests on the board will be done with the resistance/diode test
Yeah...I did it. There wasn't any change in the voltage, but I did experience a strange thing with the unit unplugged... There was about 9v of current still in the power circuits at the fuse to ground, that slowly discharged while I was testing it with the resistor.
More often then not, the power supply for devices involves a bridge rectifier and a power capacitor.
When unplugged, this capacitor will hold a charge for a while, that may be what you are measuring.
That being said, you absolutely have to make sure that the black and red probes on your meter are connected properly. Remember that voltage readings are relative...
Putting the black probe on something that is *not* a common connection to the circuit you are measuring will give you odd readings.
When you are prodding a logic board, black is typically connected to the 0V, or 'Common' connection. I know sometimes they call it 'ground', but it's not *really* a ground, because more often then not, it's not connected to the earth pin on a power plug in any way.
As far as safety is concerned, if this is something you want to learn to do, get an isolation transformer. This will make poking around safer. (not safe... but safer)