If wiggling the wire still makes any difference, it probably still isn't making a good connection to the battery.
Since you cleaned the battery terminals, check where the wire goes into the battery post clamp. Also, most cars have a connector several inches further down the Positive battery cable that is often prone to corroding. Find it, unplug it, clean it with WD-40 and a toothbrush, and then reinsert it. You may have to replace it, or cut it out entirely and splice around it.