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I realize this schematic is probably not an exact match, but the main arrangement of power components looks the same as your board: 3 large semiconductors, 2 inductors, bulk capacitors. So most of the power (Vcore) is handled by L1 L2 D1 and Q2. These beefy components are mostly lined up in a row along the outer edge of your board. Q1 handles the I/O supply, which is the large FET closer to the socket in your pictures. I would guess that this is where your 3.5v is coming from.
You can see that if the detection pin is not grounded (inside the CPU) then the 5v input to R8 will pull up the I/O feedback pin (through D2) and disable that supply. Then the core voltage (or ALL voltage on a single voltage CPU) is determined by the R4/R5 resistors to the second feedback pin. On your board, R5 is probably a parallel arrangement with whatever jumper you select from an array that can optionally raise the voltage from a baseline.
If the detection pin is floating (not connected to anything) then its exact voltage is related to the values of R6, R7, R8 and the I/O output voltage. I estimate you would measure somewhere between 2.5v and 5v; so 0.6v indicates a problem.
I've also seen cases where the detection pin will shut down the Vcore supply instead, and everything runs on the much weaker and non-adjustable I/O voltage source. You should be able to find two different feedback pins on the control chip, and follow the detection pin to one of these through a small diode and resistor network.
If your control chip is really only 5v, then some of the other small transistors may be the gate drive for the large ones. So you should be able to find 12v there. Be careful probing gate or control signals on a live board. You can inadvertently turn on a FET and put a voltage spike through the whole board.
If you can't figure out what the VRM is doing, it looks like you could remove the L2 inductor and connect your own separate VRM to the CPU side pin, and supply an independent core voltage there. You may need to add a pull down resistor to keep the mostly floating Vcore in check. If you go that route, this thread may help:
www.vogons.org/viewtopic.php?t=86611
One of the socket-VRM devices like the Evergreen Spectra would also be an easy way to do this, or at least test whether the rest of the board is working properly before going further.