After uninstalling and installing the Nike+ Connect app in multiple ways, I finally found the cause of the problem and a way to fix it.
The problem is in the Kernel Extension "/System/Library/Extensions/NikeSportWatch.kext". In Console.app I found several messages that said "NikeSportWatch.kext has no Info.plist file.".
With the Terminal.app I went into that directory and indeed there was no Info.plist file, only a info.plist file. So I renamed that info.plist file to Info.plist file and executed the command:
sudo kextload /System/Library/Extensions/NikeSportWatch.kext
And after that, as soon as I connected my watch, the Nike+ Connect software finally recognised my watch!!
The volume where OSX is installed in my case is case sensitive, but by default it's not. This might be the case for other people in this thread too?
I was having problems getting the Nike-connect software to open. I tried many of the solutions on here and stumped nike tech support. I was running Snow Leopard 10.6.4. I tried updating to the latest OS but once I got to 10.6.6, everything worked fine. I hope this helps someone. It took hours of trial and error and much frustration for me to get it to work on one of my two computers. Good luck.
I tried this but couldn't find the "show pkg. contents" ...however I just installed it as I would do normally and Praise the Tech Gods, it worked. Nike and Apple must have had lunch together and fig. it out. Many thanks to all to tried to help, I can finally upload to my own computer. So happy. Thanks all. Y.