Circuit board troubleshooting? (loose capacitor)?

Yes replacement of the bad caps is needed, they should never be able to rotate, even if the outer jacket was loose it would likely indicate that cap had overheated perhaps. Simply put, order new caps and replace them.

Snoopy, Gemma and Fifty don't know what they're talking about. On a circuit board with many components connected to a common supply point, it is impossible to go from one component to the next to see which one kills the voltage. The measured supply voltage will be the same at every point on the board that used that voltage. In other words, if the 5 volt supply is loaded down to 0.2 volts, you will measure 0.2 volts at the power supply point of every component that uses it. I would first check for which IC chip is hot. Verify that the 5 volt supply is good AND strong enough to supply the circuit. If it's a 200mA supply and you need 2 amps to run the circuit, there's going to be trouble. First the voltage will drop a lot and the supply will get hot. If the supply has the balls for the job and still gets sucked down quite a bit then there almost has to be a component eating the power. That results in heat, usually a lot of heat. If the 5 volt line measures almost exactly zero volts then there most likely is a short between the positive and the return somewhere on the board. Check the solder connections with a magnifying glass and strong light. Look at the component side of the board for shorts between connections, perhaps a small stray piece of wire shorting a component. Good Luck!

The capacitor leads are connected to the plates inside on it. If the body of this is turning this doesn't mean that the connections are already broken. This due to the metal plate body is loosely attached to the insulators. As long as no oil coming out in this one, so this is still OK. By the way I am referring the electrolytic type capacitor.

Yes;

If capacitor is turning, it has lost connection to pad or through hole via. Capacitors are made with multi layers and their elctrodes are attached to each plates. It looks like that it has broken down few layers and rotating freely and that means no connection.

had a marantz 2275,,,,,with 2 capacitors,tried burning tiny holes in plastic on each to put a tiny bit of lubricant on mvg part,,,,,,,did not work,think corroded capacitor oughta be replaced

just resold them and the problem will be solved!!