IFE
Lyman,
The Cabin Equipment Center is in the forward EE bay, so I doubt it is powered by the APU battery.
From some training material I have:
7. If the miscellaneous equipment cooling system detects smoke, the COOLING
LOSS light shows and IFE is powered off.
- The airplane must be on ground and smoke cleared to turn the system back on
I think the answer's right there...