Does the set turn off, or just the backlights? If the set is shutting off, most likely a bad power supply. It could be the digital main board, but that's less likely. It could also be the inverter board, or the panel, but that's even less likely.
Bad caps in the power supply usually result in the set not powering on, or taking several times to power on. As you said, the vented caps would be obvious if they were bad.
On your set the power is called the MPS CBA, part# 1ESA14382
Or you may have a combined power/inverter board
Inverter Board part# 1ESA17931 ( or 1FSA14240)