Ted Mayer, go through the steps systematically:"Method 1:
Try changing USB ports.
Try using a different dock connector to USB cable.
Make sure that you are using the actual USB or the original.te
Try connect directly to the white Apple USB dock connector cable.
Try update your iTunes to the latest one.
If the issue still appears try method 2
Method 2 :
1- Connect the device to iTunes, then put your device in Recovery Mode. using the steps below
Connect your USB cable into your computer.
Turn your iPhone off by holding the power button down until you see “slide to power off”.
Now hold the Home button while reconnecting the USB cable to your iPhone. After iPhone is connected it should power on the device.
Continue holding the Home button, you will see the Apple logo appear and then finally a “Connect to iTunes” will be displayed, now is the time to release the Home button.
2- Restore and wait for the error using the guide posted here
Method 3 :
For iPhone 3G, 2G and iPod Touch 1G, iPod Touch 2G users running OS 3.1.2 can use iREB to fix error 16xx or 29:
1- Download iREB and Start iTunes.
2- Put your iPhone into DFU mode.
Hold down power button and home button both at the same time for 10 seconds
After the 10 seconds release the power button and still pressing on the home button for another 10 seconds
3- Now close iTunes and Start iREB on your PC.
4- Select your device and wait for a few seconds till you get white or a red screen on your iPhone.
5- Open iTunes then press and hold left “alt” button on Mac or “Shift” button on Windows on the keyboard and then click on “Restore” button in the iTunes. Select a custom firmware .iPSW file and restore it. (note: this method doesn’t require a jailbroken devices)
Method 4 :
How To Fix iTunes Error 1600, 1601, 1602
if the above steps don’t solve your issue try to resolve it by disabling, deactivating, or uninstalling third-party security, antivirus, and firewall software on your computer." from here. I have had some good results with iReb, but have had the 16xx error with a bad battery as well. Hope this helps, good luck.