iPhone 4 won't power on with the back cover on

This past weekend I replaced the battery on my iPhone 4. I followed the directions here on how to replace it and once I had the the phone put back together it would not turn on. So I again followed the directions and took it back apart and then put it back together and again no power. I repeated this process 2 more times with the same results. Finally I tried it once more except this time I attempted to turn the phone on before I had the back cover on and it power on! So I turned the phone back off and installed the back cover but once it was on I was back to not being able to turn it on again. I removed the back cover again and tried to turn it on but still no power, so I disconnected the battery connector and reconnected it and again with out the back cover on it powered on. It seems to me that when the antenna contact makes contact with the back cover the phone refuses to turn on. Has anyone else experienced this? I'm just very frustrated at this point as I have followed the directions on replacing the battery and have been very gentle with the phone. No banging on it, no drops, no water damage ever, in fact the only problem that I had was that the battery was losing its charge very quickly as I have had the phone since the day that the AT&T 4 came out. Any feedback on this would be greatly appreciated!