Post a picture (or a few) of the PSU with the top off once you open it tomorrow (today, now that it's early AM hours here? 😁 )
If the PSU has hot glue (which it probably won't, as I don't recall Enermax or any of the better-known PSU manufacturers to use for holding down components), then there's no need to remove it. Hot glue doesn't go conductive like the organic tan glue does. Only the organic tan glue (turns brown/black when its exposed to high heat over time, and that's when it becomes conductive) needs to be removed. Silicone can also stay. IIRC, Enermax used both throughout the years. A picture should be telling enough, though.
As for the whine... yes, it may be a cap or two - probably on the 5VSB output, as that's the only supply that's On when the PSU is in soft-off mode (connected to AC power but PC not turned On.) The reason the whine may stop with the PC On is because once the main PS (5V, 12V rails, and etc.) starts inside the PSU, any load on the 5VSB from the motherboard is often relieved and thrown onto the 5V and 12V rail. Thus, with less load on the 5VSB output, the 5VSB circuit stabilizes and doesn't whine anymore.
Of course, the whine could also be normal too. I have a few PSUs and also an LCD monitor that whines quite A LOT when it's turned "Off". For these, it's simply the standby supply "pulse-skipping" or working at an alternate frequency due to a lower/different load. So a whine may not necessarily be detrimental.
With that said, one tip I'll give you is to never blindly plug-in an old PSU into a motherboard. First always plug it in AC power without a motherboard attached and measure the 5VSB output voltage with a multimeter. If all is well and 5VSB is reasonably close to 5V (I usually expect 4.95 to 5.15V), then next step is to load the 5VSB with a slight load. For this, a 12V 20W incandescent or halogen lamp will do. Connect that between 5VSB and ground and measure the output voltage of the 5VSB rail again. If the 5VSB is still relatively close to 5V (OK to see it drop 0.1 to 0.2V), you're in business. If not, open the PSU and check if for bad caps.
Actually, it's always a good idea to open any used ATX PSU you get and check it for bad caps. There's always the possibility the 5VSB supply (and caps) could be good, and something else bad. So just get in the habit of voiding the (expired) warranty. 😉 If it doubt, post pictures online.
Opening an ATX PSU is safe for the most part, if you take the following precautions:
- Always disconnect / unplug the AC power cord before opening the PSU (or any electronic device for that matter)
- Keep fingers away from internal components, especially from the heatsink(s) on the primary side (the high-voltage side that is not isolated from AC power.)
- Measure DC voltage across primary cap(s) (or bridge rectifier if easier to get at) with a multimeter to make sure they are discharged. Generally, though, if dealing with an ATX PSU that has 2x 200V -rated caps and a voltage-selector switch, then chances are that it will not have an APFC circuit and those caps will usually have bleeder resistors that typically discharge the caps within seconds of removing AC power from the PSU. But if you see a PSU with a 400/420/450V primary cap(s), beware, as those sometimes don't have bleeder resistors and may hold charge for days or even weeks. If dealing with one of those PSUs, you can still open it and work on it, but just avoid touching primary-side components that may have direct connection to the primary cap's terminals.