Without actually listening to the song, there are a few facts you might not be aware of, misconceptions about which could easily lead to the qustion you ask.
The whole point of a chord is the several note blend together and become unified, united. The notes sound as one. On an equal-tempered instrument (piano, guitar, etc) most of the intervals are actually just a little bit out-of-tune with each other. This results in the individual notes becoming more distinct: it's easier to identify the separate notes that compose the chord.
With other tuning systems (Just tuning, Helmholtz tunings) the blending effect can be intensified so many notes unite into a sonic pattern from which the separate notes are very difficult to pick out. With the explosion of computers and digital synthesizers, this territory has been opened-up for colonization.
Often the strongest note you hear (the "melody" of the chords) will be a third or a fifth rather than the root due the effects of "voice leading" or counterpoint.
When you're trying to figure out the chords to a song, 99% of the time you should try to listen for the "bass-line" and ignore everything else. The bass may not play the roots of all the chords; but 99% of the time it will play the root every time the tonic (the Key chord) comes around.