It is very difficult to point the faulty hardware without cross-testing them.
However, 3 beeps point to memory errors. I would start with this initially.
Even on Kingston website, the memory that you are using is not validated and tested on the Intel (R) Desktop Board DP67DE.
The one which is validated and tested is same like the one recommended by CMTL.
I noticed that they recommend the full height instead of the low-pro which I have, seems to have the same construction.
Standard 512M X 64 Non-ECC 1333MHz 240-pin Unbuffered DIMM (DDR3, 1.5V, CL9, FBGA, Gold) H type
Standard 512M X 64 Non-ECC 1333MHz 240-pin Unbuffered DIMM (DDR3, 1.5V, CL9, FBGA, Gold) low pro
The Adata is however the correct module for that board, near as I can tell.
If ordering the full height modules is the way to test then I'll do it. I'm waiting to hear back from Kingston first.
Thank you for your post. I have same issue. And I found a document in Intel web.
I hope your problem already solved. However, I will try other full height module. And report if this issue solved.