A little history. I've been running a Biostar TA790GX 128M with a Phenom II X3 720 unlocked and overclocked to X4 3.6 GHz at 1.4V for about a year now.
Recently, I switched on my computer and a power surge destroyed three of the MOSFETs on my motherboard. The system would boot with default settings, but if I tried to unlock the fourth core it would not POST. I chalked this up to the damaged board. Well, I replaced the motherboard with another TA790GX 128M, and tried unlocking the fourth core of my Phenom II. The system will not finish POST -- it gets to the first step and hangs until the CMOS is cleared.
Did the MOSFET failure damage my processor?
Three of the chips literally exploded and burned. The MOSFETs had an Enzotech MST-81 heatsink on them, adhered with Arctic Alumina thermal epoxy. Worst case here is the CPU will no longer unlock or overclock. I have not attempted to overclock yet on the new board because the MOSFETs are not heatsinked.
MOSFETs are designed to handle a maximum amount of power. If the power is pushed even slightly beyond that limit (i.e. power surge) then the MOSFETs are at risk of failure. Obviously this is what happened.
Now, the function of the MOSFETs is to regulate the processor's power. When they were destroyed, the CPU may have caught some of the power surge.
AMD's x3 processors are technically all (or nearly all) x4 processors that have been crippled for some reason, either because they are not up to standards, or to meet demand. Because you cannot unlock the 4th core, I think it is safe to assume that your chip was one of the ones that was not up to snuff, but was still strong enough to run when you unlocked it. Therefore, it would have been more susceptible to the surge, and could have been cooked.
Checking with a new motherboard only confirms this. If the system has identical components, then you most likely have a dead core.
To confirm, I suggest testing the new motherboard with a known overclockable / unlockable CPU from another machine. This should eliminate the possibility that it is a motherboard issue. Also, make sure that the BIOS version is the same on both motherboards, the old and the new.
In short, it seems very likely that you have damaged your CPU, but without further testing there is no way to know for sure.
One more thing - If you decide that you have damaged the core on your CPU, I would not suggest trying to overclock. The entire CPU will probably be more sensitive, and a voltage bump for overclocking could be dangerous.