i doubt it's the caps, need more digging
from pdf i see only one led for each voltage (12 and 5V, page 2-6 D53-D54), that implies only those 2 power rails (meaning molexes are parallel) but you say it's 4 power rails, 2x12V and 2x5V
in that case, you need to diagnose the 2'nd set of 5V, maybe you got some 3v3 regulator failed or something derived from that 2'nd 5v rail who is shorted
viewing the quality of the caps in such products, i doubt you will find died caps, but maybe failed semiconductors, like some dc-dc or why not, sas controller chip
you have one working side, so identifying seems simple enough, just tracing the 5V loads on each 5v rail
but my bet is one 5V rail, and you have to look on 5V derivates/2'nd sas controller