You said 1 board is working, so, have you checked complete reads,writes and initialization with this. So,that we can take this configurations(all registers and other stuff) as reference.
In Non-Working board,
I assume powers are OK within specifications (mainly Vref to both DDR2 and controller)
Can u check CKE# to go HIGH and CK/CK# is running, during interface initialization as per Jedec spec.
In JESD79-2F page 27, there is a initialization procedure,
mostly programming EMR registers require either of BA(bank address inputs) toggling, or A10 toggling..
Check whether A10 or any Bank address signals are toggling or not?
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If we are confident that assembly is not an issue...then it's OK....
Otherwise please check impedance's of rails VDD,VREF and important lines like DQS,any of DQ, any of address lines to see internal shorts.....
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