Inductors can also make a higher pitched noise, to isolate the noise you need access to the area and to firmly grasp and press on it between your fingers. Sometimes just firmly pushing on the side you can find the culprit, with something non-conductive like a stick or toothbrush handle.
Hot glue isn't a great idea, some of them get rather warm and it can melt off and make a mess, plus since it seems likely you won't be able to 100% cover them, that hot glue or silicone still allows them to flex some it so with partial coverage it might not be effective. Because of where they are ( example picture -
http://img.hexus.net/v2/mother...a/images/board-big.jpg ), it may be difficult to apply anything with it in a case. I would take it out of the case, put the board perpendicular to the table-top propped up so the rear ports are facing up, then apply epoxy to the larger, green and yellow one next to the northbridge. You'd have even better access to the other side of the green one if you took the northbridge 'sink off, and capacitors are in the way for the rest of them so all you can easily do is push as much epoxy into the hole in the center as possible to make it flow out the other side a tiny bit.
Yes drench them all if you want to do it all at once, though you should try to keep the epoxy off the board and adjacent caps so they, and the inductors you're covering, could be desoldered and removed if they later needed to be. Also keep in mind it's possible the lan ports have magnetics inside their shell which could be what is making the noise, ideally you need to figure out which one it is first. With some noises putting a straw or piece of tube in your ear and placing it next to suspect parts can help pinpoint the source, but with high pitched inductors it is more difficult.
If you're confident that you would never desolder the inductors there is an easier way to apply the epoxy. Make a form out of paper, an oval 0-shaped loop such that the bottom edge sits flush against the motherboard, with a large enough diameter that it slips over the inductor with just a little room on each side. The board has to be sitting parallel to the desk so gravity does the work for you. With this form in place you can very slowly pour or dab-in slow-setting epoxy to fill the form up to the top of the inductor then leave it there until it has set. If you wanted to get fancy about it, you could use a piece of packing tape instead of paper, then with the sticky-side in, after the epoxy sets the tape will peel off. Normally dabbing some epoxy on inductors isn't as difficult without making a mess but those are in a bad location. Just about any typical epoxy would work, even those not heat-rated can stand the level of heat present. I usually use JB-Weld because I try to keep some around, but have used other stuff too without any problems so long as the epoxy sets slow enough that you aren't in a rush. If you will be dabbing it on without a form around it, a faster settting epoxy may reduce it running down and getting all over the surface of the PCB.
Obviously these things void warranties, if your warranty is good still you might see if they'll replace it.
