sql server if statement not working

You don't need an if statement - you can just run the update statement, and if the subquery returns no rows, no rows will be updated. The if won't really save anything - you're performing two queries instead of one.

You either want

UPDATE TBL_SystemParameter 
SET [Value] = 'Ping.wav' 
WHERE ID In (SELECT ID 
        FROM TBL_SystemParameter 
        WHERE code = 'SOUND_WRONG_GARMENT')

if there are multiple ID's with that code OR use

UPDATE TBL_SystemParameter 
SET [Value] = 'Ping.wav' 
WHERE code = 'SOUND_WRONG_GARMENT'

either way and lose the IF statement as @Mureinik said.

Although Mureinik's answer is the logical solution to this, I will answer why this isn't actually working. Your condition is wrong, and this approach will work instead using IF EXISTS:

IF EXISTS (SELECT * FROM TBL_SystemParameter WHERE code='SOUND_WRONG_GARMENT')
    BEGIN
        UPDATE TBL_SystemParameter 
        SET [Value] = 'Ping.wav' 
        WHERE ID IN (SELECT ID 
            FROM TBL_SystemParameter 
            WHERE code = 'SOUND_WRONG_GARMENT')
    END

As a side note, you're using an = sign instead of IN, which means you'll be matching to an arbitrary singular ID and only update 1 row based on this. To use a set based operation, use the IN clause.

You could actually 'golf' this by doing away with the derived query altogether, and using a simple WHERE code='SOUND_WRONG_GARMENT' on the table you're updating on.