I don't know if it is only my issue. I have a 2011 iMac i5 with 2x2GB RAM modules.
Recently I bought 2x8GB RAM modules. If I add the 2x8GB to the default 4GB RAM, the computer doesn't start. I hear only the sound of DVD slot but the screen remains blank.
If I remove the 2x2GB ram modules and I use only the 2x8GB RAM modules, everything is fine and the iMac shows correctly the 16GB. I have also tried to change the order, putting the 8GB modules as first, but same problem.
If I put 2x2GB with the 2x8GB together, iMac doesn't turn on.
Original RAM: 2x Elpida 2 GB PC3-10600s-9-10-f1
Upgraded RAM: 2x Hynix 8 GB DDR3 Dream 1333mhz SO-DIMM (sold as Apple iMac 2011 compatible)
The original RAM was mounted on top 2 slots.