Yep, I'm pretty much sure it wasnt the alternator now, but I have no clue what else might have caused it. I inspected the connections, they seem fine.
What I am going to do now, is replace the cables from alternator to the battery with new, heavier gauge wires.
Now, about the alternator, I already have the new higher juice alternator, so I'm just thinking whether to install it or return in. I mean, the original alternator is bound to go sooner or later, it already has 145k miles on it, and typically these things do not even last that long. I don't plan on getting rid of the car any time soon, so might as well replace it.
My question is, what kind of benefits am I going to see with higher juice alternator? So far, with the original one my lights are getting dimmer when I run other accessories, such as AC, rear defrost etc. I would assume with new alternator that shouldn't happen.