Impossible to say. If the defect sits with the CPU, then most likely... if the issue is the motherboard, then likely not.
Clearing the CMOS would've achieved what I was suspecting... so if you're still seeing 1/2 rather than 2/4, there's not likely to be anything within the BIOS that'll 'fix' it, but I'm not familiar with that specific BIOS.
If there was anything, I'd assume it would be something along the lines of "Active Core" based on other AMI BIOS', but for an OEM intended FoxConn board, it could be anything.... Should be relatively obvious if there is anything though.
At this stage, you could explore updating the BIOS.... &/or, consider reseating the CPU and checking the socket for bent pins.
You'd need thermal paste to reinstall the cooler optimally, you could get by temporarily just reusing whats on there if you really had to.... but I'd highly recommend picking up some thermal paste.