The key is already the ... ehm ... key

echo $array[20120504];

If you are unsure, if the key exists, test for it

$key = 20120504;
$result = isset($array[array[$key] : null;

Minor addition:

$result = @$array[$key] ?: null;

One may argue, that @ is bad, but keep it serious: This is more readable and straight forward, isn't?

Update: With PHP7 my previous example is possible without the error-silencer

$result = $array[$key] ?? null;

Firstly, this could use a better description (in a comment) explaining what it does. I had to figure it out from the code. I think the description should probably be something like

// Searches $array for associative arrays which are supersets of $parameters.
// If $multipleResults it will return all matches in an array;
// otherwise just the first, in an array.

Secondly, names.

• findValue isn't very descriptive. How about findSupersets?
• $array would traditionally be called $haystack in PHP, since you're searching through it for matches to a predicate.
• $multipleResoult is a misspelling. Correcting the spelling and adjective-noun agreement we get $multipleResults, which is ok, although I personally would prefer to communicate an action: $returnAll.
• $suspicious has the wrong connotations for this native English speaker. If something is suspicious, it means that I think there's something wrong with it. My preferred variable name for something which may or may not pass an acceptance test is $candidate.

Thirdly, since PHP has a dynamic type system I think it would be more idiomatic to return just the element if !$multipleResults, rather than wrapping it in an array.

Now, you specifically ask whether there's a simpler way to do it. I think that using booleans it can be simplified quite a bit by inverting the assumption. Rather than prove it acceptable, prove it not acceptable. Taking into account various of my suggestions above and refactoring I get:

    foreach($haystack as $childArray){
        $isCandidate = true;
        foreach($parameters as $k => $p){
            if(!array_key_exists($k,$childArray) || $childArray[$k] != $p){
                $isCandidate = false;
                break;
            }
        }
        if($isCandidate){
            if(!$multipleResults){
                return $childArray;
            }
            $result[] = $childArray;
        }
    }

    return $result;

It's a couple of years now since I used PHP, and I'm not sure offhand whether there are built-in functions to test whether $childArray contains $parameters as a subset, or to filter an array by a predicate. It may be that the whole function can be reduced to two calls to built-ins. If not, you could consider whether you want to factor it out as

function findMatch(array $haystack, $predicate, $returnAll = false) {
    $results = []
    foreach ($haystack as $element) {
        if ($predicate($element)) {
            if ($returnAll) return $element;
            $results[] = $element;
        }
    }
    return $results;
}

function isSuperset(array $candidate, array $subset) {
    foreach ($subset as $k => $v) {
        if (!isset($candidate[$k]) || $candidate[$k] != $v) return false;
    }
    return true;
}

linking the two with a lambda.

Code:

function search($array, $key, $value)
{
    $results = array();

    if (is_array($array)) {
        if (isset($array[$key]) && $array[$key] == $value) {
            $results[] = $array;
        }

        foreach ($array as $subarray) {
            $results = array_merge($results, search($subarray, $key, $value));
        }
    }

    return $results;
}

$arr = array(0 => array(id=>1,name=>"cat 1"),
             1 => array(id=>2,name=>"cat 2"),
             2 => array(id=>3,name=>"cat 1"));

print_r(search($arr, 'name', 'cat 1'));

Output:

Array
(
    [0] => Array
        (
            [id] => 1
            [name] => cat 1
        )

    [1] => Array
        (
            [id] => 3
            [name] => cat 1
        )

)

If efficiency is important you could write it so all the recursive calls store their results in the same temporary $results array rather than merging arrays together, like so:

function search($array, $key, $value)
{
    $results = array();
    search_r($array, $key, $value, $results);
    return $results;
}

function search_r($array, $key, $value, &$results)
{
    if (!is_array($array)) {
        return;
    }

    if (isset($array[$key]) && $array[$key] == $value) {
        $results[] = $array;
    }

    foreach ($array as $subarray) {
        search_r($subarray, $key, $value, $results);
    }
}

The key there is that search_r takes its fourth parameter by reference rather than by value; the ampersand & is crucial.

FYI: If you have an older version of PHP then you have to specify the pass-by-reference part in the call to search_r rather than in its declaration. That is, the last line becomes search_r($subarray, $key, $value, &$results).