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The DH61BE supports 8GB DIMMs since BIOS 0020 and the readme of the latest BIOS update also claim that memory issues were resolved. 3 beeps does indicate a memory problem.
I don't think 1600 Mhz is the problem as this is just the max speed and the board can select 1333 Mhz. But if have have a BIOS before 0020 then one 8GB DIMM is probably the problem.
You could try to use a temp 4GB DIMM to start the board, check the BIOS version and update it if a newer BIOS version would potential solve the problem.
P.S. The technical manual of the DH61BE was updated to claim that 16GB is now supported with just two 4GB DIMMS, seem that someone was sleeping when they did the update. The revision history even states that the support was improved from 16 GB to 8GB