Upgrading 16 GB to a 4 GB iMac i5 2011 doesn't work with all modules loaded [SOLVED]
I can't find an exact diagram for the iMac, but assuming the mapping is anything like my Mac Pro - which really surprised me when I first tried it, the top &amp; bottom slots may not be as you expect.

I would certainly experiment with identical RAM first in top or bottom, but I would also try matching them top to bottom row

ie…

2  2        8  8
8  8   or   2  2


but also 

2  8        8  2
2  8   or   8  2


I would also reset the SMC between each test.


Shut down the computer.
Unplug the computer's power cord.
Wait fifteen seconds.
Attach the computer's power cord.
Wait five seconds, then press the power button to turn on the computer.


This is the odd layout for mine - yours will not be the same, of course, as it has fewer slots, but might follow a pattern…
see how the config changes between 2 &amp; 4 DIMMs, contra to what 'common sense' might make you think

Two DIMMs      One on the top memory card and one on the bottom card  
Four DIMMs     One pair on the top memory card and one pair on the bottom card  
Six DIMMs      Two pairs on the top memory card and one pair on the bottom card  
Eight DIMMs    Two pairs on the top memory card and two pairs on the bottom card