So I tried playing the songs Amazing Grace (from my guitar lesson book), the Slamdunk Opening 1 and Simple and Clean(chords). All these songs go with chords.
When I learn the songs, I look at the chords, find the ones that I have an easy time playing, and strum on the rythm with that chord.
But I can't hear/imagine the song in the chord(s) that I'm playing. Does that make any sense?
Is it my guitar? My amplifier? My general sound?
I really don't want to drop chords, because I have a feeling they can be very important.

But when I try practicing the tab version of Simple and Clean(Utada Hikaru), and Whole Lotta love (Led Zeppelin), I don't have this problem. :S
Have you tried singing the actual melody over the top? Unless it's either a chord melody piece or has a very distinctive chord progression it can be hard to identify any song from just the chords.

I don't know the Utada Hikaru song but the Zeppelin has a riff and not just a set of chords so it's easier to hear the song itself.
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Quote by Master Foo
“A man who mistakes secrets for knowledge is like a man who, seeking light, hugs a candle so closely that he smothers it and burns his hand.”

^ This.

You identify a song usually based on the melody. If you're going to be playing just the chords (which, incidentally, can be the very same chords for thousands of other songs), identifying the song is going to be quite difficult.

Have you tried playing the chords with the song in the back?
^No, I haven't thought of that XD XD. I'm going to try that as soon as possible.