Characters like Kyle Rayner from war of light possess the following trait:

CONSTRUCT: When building your force, you may attach a construct (Lantern) to this character by paying its point cost. Give this character a power action and replace the construct with any other construct, up to 2 points higher than the original construct. If this character has no action tokens and the new construct is a lower point value than the original construct, this is a free action instead.

ok what I'm asking here is: since contructs are part of resources (power batteries) can I play a character like Kyle Rayner starting with a construct attached and play a resource which is not a Power Battery (like, for example the Infinity Gauntlet)?

The Construct Trait Construct is not part of a construct. So it does not prevent you from using a resource.

Constructs aren't relics, so there is nothing restricting their use with resources....

They arent considered tactics either, so they're good to go for no tactics events.

I think they are considering a different answer, but the others are right as of what we have right now.
The reason I say that are because of http://www.wizkidseventsystem.com/bb...php?f=3&t=3855 and http://www.wizkidseventsystem.com/bb...php?f=3&t=2277

Correct, but it's always best to check with the judge on that first. Entities are not tactics, but they are considered as such by many venues running a no tactics event.