It's a start! Keep going - I personally think everyone could be composing music if they had the drive, but like any artistic skill, it takes patience to get somewhere with. Try lots of styles and instrumentations and techniques to find a voice - what you love composing may not be unbelievably popular in any 'scene' you point at, but if you don't love what you're making it'll come through in the music. Don't let people tell you it's not a good career choice if you're really interested in it, either, there's plenty of wiggle room between nobody and superstar, and plenty of musicians have day jobs
as musicians for projects that need something more specific than stock jazz #87.
I'm curious what software you're using. Having branched out from acoustic guitar to electronic music, I personally started with PowerTab (sadly non-functional on win7 last I tried), and then my brother got me into FruityLoops/FL Studio. I've also used
LMMS for one track, which is free and useable enough that I could make something in it my first try without a lot of grief, though I didn't work with it long. Other people will tell you to use Reason, but I found it clunky for non-sample-based work.
The reason I ask is that, especially for piano, throwing in reverb (convolves the sound to create a feeling of atmosphere) and a subtle low-pass filter (clips off higher frequencies with a little bit leaking through) can help make it sound much less artificial. Also, it sounds like you're using stock midi - as soon as possible, get a VST plugin like
PianoOne, the results are much more pleasant and dynamic if you vary the velocity (volume) of each note. There are also other midi patches available - the
General User GS soundfont is pretty nice for what I call 'sketches', to make a melody in a familiar instrument if I'm not quite sure what voice I want to use, and I also like diving into the
HammerSound library for more esoteric stuff like bodhran, etc.
If you need help setting anything up or have any questions, let me know.
edit: one other thing... you say there are parts that bug you, you can identify those parts, so figure out why! It took me more than ten years to realize that no one will tell me why but me, that I had to experiment by tweaking every part in a section, sometimes parts before or after that section, to work out why something wasn't working. It's very difficult to critique music in a way that the musician can use - I personally liked the dissonance of what you made or I wouldn't have commented, but that may be exactly what's annoying you.