Hi,
I'm completely new to this forum, in fact this is the first thread that I've read, but my reaction to this thread has been so strong that I felt compelled to join and write a (quite possibly way too long..sorry in advance) response to it.
What Nick seeks, contrary to the opinions of many posters in this thread, I believe is completely achievable, and I can't believe that there haven't been more people helping him out. So here's my take on it.
All you need is an understanding of some basic musical concepts.
1. A piece of music is in a keycentre.
2. The notes of that piece of music will mostly come from the major/minor or another scale that is built on the tonic note of the key centre.
3. Most of the harmonic movement is outlined by chords made up of notes from the major/minor scale of the piece. These are called the diatonic chords.
This is basically all the theory you need to get started. Try playing a C major scale. Now play any diatonic chord from that scale - C maj, D min, E min, F maj, G maj, A min, B dim (notice that these chords all only use the white notes of the piano - the notes of the C major scale.)
Try moving between these chords. Start with C major, and return to it relatively frequently, as it's the tonic chord. F maj (the IV chord) and G maj (the V chord) will also sound very natural, especially going from G maj to C maj (the V - I progression - a perfect cadence).
Try making up different chord progressions like this, and creating your own melodies using notes from the C major scale. You'll be making up your own music in no time.
You can advance on this by learning how to modulate to a new key centre, or learning how to use chromatically altered notes (the black notes when we're in C major).
This, in my opinion should get you started. To make the tunes that you play more interesting, you can improve your voice-leading between chords if you don't feel it's great, learn new voicings for the chords, learn to play them in new rhythms, or find new ways to outline the chords melodically rather than playing them in blocks.
You can learn to recognise the chords and melodies as you hear them in your ear with some ear training. Contrary to popular belief, training your ear and learning to play by ear require no talent whatsoever. Anyone can do it. The course that we've developed at Ear Training HQ is designed to allow you to do this easily, and with it you'll start to learn to identify things in music very quickly.
Anyway, that's my 2 (or is it 10 or 15 cents). You can find out more about our ear training method at our website, and you'll probably find the information in our free video series: Ear Training Essentials useful for what you wish to learn. (Sorry about the shameless plug, it's only because I feel it's relevant)
https://www.eartraininghq.comAnyway, I think that's about enough from me. I hope this information is useful for some people
(and I hope I haven't broken any forum rules by putting a link to my site in, I didn't see that it's against forum rules so I figured I'd just put it in.)
And as a P.S. - I found this thread because someone contacted me through Ear Training HQ asking for resources to help them learn to play basic piano. I assumed when I read the original post that I'd get a list of great books that would help Nick to play in the way that I described, and I couldn't believe it when there seemed to be barely anything of that nature. So if anyone does know of a book that teaches piano in this way, please post it!