I am going to make a wild guess here that the Dell dock is also plugged into your computer via USB, that for some reason the dock is actually charging from the usb rather than the wall charger when both are connected and that your PC doesn't provide the proper minimum current to the usb port when both items are plugged in.
If I am right then you may be able to fix this IF
your PC has more than one USB controller built in. If you have more than two usb ports move the connecting cable of one of the devices to another USB port and see if the same thing happens.
I am thinking that there may be an internal switch on the Dell dock that 'prefers' the connection to the USB port when the USB cable is plugged in and that it not sophisticated enough to switch to the mains charger if the USB current is too low. I further speculate that the switching is done to prevent charging from both sources and that the USB is 'preferred' so that you can transfer data while charging.
Edit: or your Streak could be allergic to Apples.