I am sorry to hear that have had issues with your Intel board and processor.
In regards to compatibility for your processor, if this is not listed on the Compatibility Tool, this means, is not compatible.
I can't agree with you, please refer here - this is more accurate answer: Does DZ87KLT-75K support the Core i3-4330T?
Anyway I solved my problem, it was caused by damaged pins on the CPU socket. So I replaced the motherboard and it's working like a charm. Sorry for telling this but I'm happy for leaving DH87MC behind, these issues are really problem:
PS: Sorry for the late answer, I was experiencing some problems with login on my laptop due to site certificate.