Hello and welcome to the forum Coqui:
I don't think an old panel would lower the voltage, especially to a different level in seperate parts of the house.
I experienced what you are talking about once in the past though. It turned out to be one of the cable splices where the power company had spliced onto the house wiring at the weatherhead. A quick way to check it is to use a voltmeter at the main fuses in the panel; I think you will find one side much lower than the other. If the test works like I said, you need to call the power company to resplice the wires.