I think there have been loads of us in your position - the bottom line is that if you can speak English fluently, have skills in demand, are trustworthy and able to contribute something to society - you have zero chance of getting in.
If you're Irish, you have a slightly better chance than us English (we have a 'special relationship' which means we can go an fight wars with the US but cannot put in for the immigration lottery)
My friend and I tried the Forces route - the Army recruiters were practically foaming at the mouth when two helicopter pilots walked in and asked to join up - but after a phonecall to the bosses we were told we needed a greencard to apply.
I asked for where it said that in the rulebook, and was given a reference.
It said "in time of peace, no foreign national may serve in the armed forces of the united states" - apparently in the eyes of the US military we are at peace and there are no wars going on in either Iraq or Afghanistan!
Too bad - I was really looking forward to flying the new Little Bird.