Step 1: Diagnosing ARDS in a child requires checking several defining features together.
Step 2: The illness should begin within a week of a recognized triggering insult, satisfying the timing requirement.
Step 3: The hypoxaemic respiratory failure must not be attributable purely to heart failure or fluid overload, so the cardiac status, including any left ventricular dysfunction, has to be evaluated and accounted for.
Step 4: Since each of these considerations feeds into the diagnosis, the inclusive option covering all of them is correct.
\[\boxed{\text{All of the above}}\]