If the iMac can do a 1333 FSB, then I would think a Core 2 Quad would actually work. Assuming it is similar architecture as the Core 2 Duo being replaced. I read about someone trying this swap elsewhere, and they had no luck (no boot), but they used one generation older Core 2 Quad, which would have a higher thermal loading, and the chance of it being compatible was not that high in the first place.
One problem with this is the 21.5" iMac has a 1066MHz system bus, and the better C2D processors are 1333MHz bus speeds. If you stuck a Core 2 Quad chip in the iMac, it would probably revert down to the 1066MHz bus speed, which would significantly reduce the overall clock speed of the new processor. But, if it did work at least you would have quad cores.
If I were you I would open the computer up and try to track down where the sound is coming from exactly. Chances are it is the power supply and could be capacitor related as you stated, due to your poor quality power. The caps on the motherboard would probably be fine still, as the power supply should do a good job filtering things and your motherboard should be getting good clean power. Once you get the cover off this style iMac it is only a few screws to remove the LCD and a few more to remove the power supply You can pull the supply and check the values on it for what you need. Then put it back and mount the LCD, but don't put the cover back on until you get the parts you need. I have a 2.16 C2D iMac power supply which is dead. If it is the same as yours, I can give you the values off of it, or send you photos of it.
When you tried booting the system with no RAM and the fan ran at low speed, then with the LCD sensor disconnected and still no RAM, the fan ran at high speed, that would indicate to me the SMC is properly detecting the LCD sensor and there is no issue with the LCD sensor. But I could be wrong. I just went through all this myself last week on my iMac which I bought used and had no LCD sensor. When I finally installed my sensor, the fans went quiet. If your computer is working just fine other than the loud fan, another sensor may be the problem.
I have thoroughly cleaned every aspect of this iMac. There is no dust left. I put new thermal paste on both the CPU and the GPU. Using SMC fan control I have increased the CPU fan speed (which also cools the GPU), and the artifacts have been significantly reduced. Not gone, but much better than before. Initially when I boot the computer or return from sleep mode there are several minutes before anything shows up. I think Apple can fix this issue, and it would not cost them a whole lot. If they made an optional flash utility for these computers (my research is showing this as a very common problem), which reduces the clock speed of the core, I am sure the issue would go away. Sure our graphics would be a bit slower, but that is a lot better than an $800 logic board replacement. I once had an iMac G4 800 which was not stable until I used it in the garage during the winter. I found the PLL control resistors on the logic board and cut the iMac down to 700MHz. It was perfectly stable after than even in high...
Do the fans run loudly most of the time? There is not much space inside an iMac, and when dust starts to build up, they overheat. If you hard start it, the parts will still be warm, so you will get even less time out of it than the prior power on. You may need to disassemble the computer and blow all the dust out from the fans and off the board.
You probably already checked this, but did you make sure to align the tabs on the front of the black drive bracket with the holes (if there are any on the new drives) in the sheet metal casing? Oddly enough I was just remounting the DVD drive in my 20" 2.66GHz iMac yesterday, and I had to struggle a bit to get the tabs to snap in. If you don't have it right, the drive bracket will distort the shape of the drive slightly, and I am pretty certain that would cause retraction or ejection issues.
I have come across several laptops which would randomly shut down due to heat. Dust built up on the CPU fan would retard thermal performance to a point where the system would power off to protect itself. These computers would do this completely at random, regardless of loading. A few short bursts of compressed air to the fans solved the issue. If you do use compressed air, never blow the air for more than a second or the fans my over spin which will often destroy them.