After i-tunes quits, ipod says synching and then connected...
Your iPod is a shuffle? A shuffle has no screen, so if iTunes is not running because it unexpectedly quit, where are you seeing the iPod say "syncing" and "connected." Is it a nano?
If it's a nano (or an iPod with a screen), you can disregard the question about the LED "light." What appears on the screen is good (plus the Disk Utility and System Profiler results), because your iPod appears to be recognized properly by the computer. But there may be some data corruption on the iPod's storage that is causing iTunes to crash when it tries to do the initial sync.
If you don't have a problem with erasing what is currently on the iPod (because everything is in your iTunes library you can just resync it), you can try the following. Put the iPod into Disk Mode
http://support.apple.com/kb/ht1363
(This assumes your iPod is not a shuffle, because there is no Disk Mode for a shuffle.)
If you can put the iPod into Disk Mode, connect it to the Mac. I don't think iTunes will start up automatically. Then run iTunes. If iTunes says something about "recovery" and prompts you to do a Restore, do the Restore. This will erase the iPod, reinstall its software, and set it to default settings. If the cause is data corruption and is not hardware-related, the problem may be resolved.