Ipod Battery Issue

Hi,

I bought an Ipod just this last weekend, When I went to Charge it for its first charge I have it connected to the computer for 4mins it said do not disconnect and then I disconnected because I realized that it was to my older computer that doesn't have USB 2.0 so I disconnected thinking that it would be better to charge it to a computer with USB 2.0. I then realized that by doing that that would count as the first charge and the battery said it was full, when I hooked it to my other Pc it charged for a little bit and then stopped. Did I compromise my battery life by doing this because I know that it is lithium but I'm under the impression that even with lithium’s the first three charges are essential to charge the battery to full and then run it all the way down. What do you think? I know its not Nickel Cadium but I still remember reading that the fist three charges are important, I can always return it and get another player and say that it had a defective battery. I also notice that the battery only lasted less than 3 and a half hours on this first charge.