Is your USB drive self powered by the USB cable or does it have an external power supply?
If it is powered by the USB cable then there is your problem, the DNS-327L only just supplies enough power on the +5v USB pin to meet specifications, it is not enough to power 3.5" drives for any length of time. The 3.5" drives require a USB case that has an external power unit or a computer that supplies much more the the 500mA called for by the specs (it is 1.5A for computer mounted USB v2 sockets).