It sure seems to me that there is either a very high resistance connection somewhere. I'd start by inspecting the blades on the plug end of the cable, if they are not bright brass colored, burnish them with an ignition point file or your wife's emery board. Don't use steel wool as I have heard some experts suggest. The shards will conduct and while not likely, can cause a shock problem. Then with the cable disconnected from the system check the cable.
If the cable is bad, replace. You could try removing the molded plug is the cable shows bad and test directly to the wires. That would require a new plug but they are cheap.
From there on check every connection all the way up to the distribution panel circuit breakers.
Of course you could tighten everything first and the turn the power on and see what happens. You wouldn't find the problem if it is a loose connections but you'll have piece of mind that all the connections are secure.