This may sound too obvious but you can remove the top cover and visually inspect and see if there's a loose connection. The technical term for this is wiggle test....
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Sounds like you’ve already located the problem, tiger.
If the transformer is connected directly to the chassis, it’s likely the transformer has a flakey internal connection. If the transformer is connected to a board which can flex, the problem is likely a trace on that board which has a hairline crack (probably invisible to the naked eye: try going over the traces with a magnifier, and, if you find a hairline crack, solder over the trace at that point).
If it’s not a hairline crack, the problem is probably a component with a cold solder joint. Look for a solder joint which is duller than the surrounding ones, or a joint which is shaped more like a ball than a cone. Then remove the old solder, and resolder.
Just my 2 cents. Good luck!