Hi,
is your motherboard compatible with 1600mhz RAM?
The reason why it might be working with your other stick installed and not on it's own is that when two different speeds of memory are inserted into a motherboard the RAM will always run at the lowest speed.
So your 1600mhz stick will have been running at 1066mhz same as the original stick. If your motherboard is only compatible with that speed then any higher simply won't work.
Try checking in the bios and see if you can change any settings to do with RAM. Don't worry if your 1600mhz stick is running at 1333mhz as this is normal. One then has to overclock the ram to reach the speed set by the manufacturer.
If you post the make and model of the motherboard we'll be able to tell...