I just bought a Arduino Ethernet W/O PoE + USB2SERIAL from seeedstudio for my first Arduino project. I connect the usb2serial to the Arduino and plug a USB cable from the usb2serial to my (Ubuntu) computer but nothing appears in lsusb and nothing appears on dmesg. However, the power LEDs go on on both the converter and the Arduino.
It's beginning to sound like your USB2SERIAL (or the USB cable) is defective. Try it without the Arduino attached. If at still fails, you should contact the seller about a refund/replacement.