I can only give you some general advice without seeing what you have (could you perhaps post a photo or two on Facebook?). Someone with a service manual could tell you more if you provide the part identifier printed on the board (for example, a resistor might have a label next to it or under such as "R357", while a transistor could be "Q241").
The part that is overheating may be the problem, but more often it is getting hot because another part has failed and is causing too much current to go through the overheating part.
If your set has the typical CRT rear projection TV layout, the board in question is a high-frequency switching power supply. The noise you hear may be from an overloaded transformer. A very common failure mode in these power supplies is a shorted diode on the secondary side of the transformer (the side away from the power input). This will cause an overload on the primary side and put it in some form of current limiting mode (in many designs it just blows a fuse, but in some current is limited by electronic protective shutdown circuits).
Finding a shorted diode is not difficult if you know how to use an ohmmeter and can identify a diode (the board marker will be "Dnnn"). A good diode will have a large resistance or read open if the test leads are connected in one direction, and have a smaller resistance in the other. A bad diode will read close to zero resistance in either direction. CAUTION: resistance tests must be made only with the set unplugged! Attempting to read resistance on a live set can cause severe damage to the ohmmeter, and could blow up the power supply, to say nothing of personal hazard from the high voltages present.
Here are a couple of typical diode packages:.
This part is usually mounted on the board, sometimes on extended leads so it has some airspace between it and the board for cooler operation. The image shown is about size of the largest examples of the DO series package type. Note that there is a band painted on one end of the diode. If you connect the minus lead of the ohmmeter to this end and the plus lead to the other end, you should get the lower resistance reading mentioned previously.
The TO-220 package is shown about the actual size. It is also used for transistors, voltage regulators and other power integrated circuits, and (rarely) resistors. The center lead is often bent outwards to fit a triangle hole pattern in the board, and the tab is fastened to a metal heat radiator of some sort. Use the board marking to identify the part (if it doesn't start with "D" it isn't a diode), or look up the part type number online (printed on the front of the package). Often there will be two diodes in the package sharing a common connection to the center lead. The center lead is usually equivalent to the banded end in the DO-type diodes. Note that transistors also often fail by shorting out. Once in a while the failure is obvious - the plastic will be cracked, burned, or even have a crater blown out of it.