|Apparently this is a fairly recent USB connected external drive.|
Has this drive ever worked properly previously for you??
1. Most burning software programs have a simulation mode - that goes through the motions of burning, you see the same things, but doesn't actually burn anything to the disk - make sure you have the program set so you are actually burning.
2. See the label on the bottom of the drive - you'll probably see it requires 500ma or close to it. Your external drive requires that it can get enough current from the USB port it is plugged into - if it can't get enough current from the port, it probably WILL NOT work properly.
External drives require a lot of power, and they won't work properly in all possible USB ports you can plug them into.
The USB connection of the external drive requires that the USB port you plug it into can supply 500ma, the max. USB spec.
The front USB ports in a desktop case may have inadequate wiring to them. If you have USB ports higher up on the front of the case, the wiring for them may be inadequate, or the multiple ports may be ports in a hub that connects to one USB port directly connected to the mboard - that type of hub does NOT work properly with all USB devices.
If you have the drive plugged into an external hub that is the type that has multiple ports that connect to one USB port directly connected to the mboard, the external drive and many other USB devices may not work correctly, even when the hub is a "powered" one that has an external power adapter connected to it. The same goes for USB ports on a printer, scanner, keyboard, etc. which are ports in that type of hub.
The external drive can get enough power from any USB port directly connected to the mboard on a desktop mboard, and directly connected to the mboard ports on most laptops. If you have a plate in a desktop slot space with USB ports, that will probably work with an external drive, if the wiring to the mboard header is adequate. The ports in a PCI USB controller card can all supply enough current. Some laptops can't supply 500ma from any of their directly connected USB ports - in that case you have to connect an external drive to TWO USB ports, or one USB ports and have an external power adapter plugged into a jack for that on the drive.
Some external drives come with a USB Y cable - a small USB plug on one end, and two regular type A plugs on the other end. According to pictures of your model I found, it looks like your model DOES have a USB Y cable, and it does NOT have a jack for an external power adapter. If you are connecting this drive to a laptop you MAY need to connect it to TWO USB ports.
An external drive may not work correctly when plugged into a port on a laptop's PCMCIA (PC Card) USB 2.0 controller card, or a port in an ExpressCard USB 2.0 controller card, even if the card has a jack for connecting an external power adapter to and you connect one.