That was an excellent remix! I'm gonna put it on my mp3 player. lol I don't find the lead synth to be whiny, in fact I think it fits perfectly with the overall tone of the remix. I have to disagree with earlier comments that's it's too repetitive. To me the chord progression and the lead synth are what make the original. Take them out or use them any differently and you no longer have a remix.
I'm kinda new to the field of game remixes. I've actually wanted to do something with this song for ages now, but I can't find the sheet music or a midi file. Did you sample the original or play it by ear?