I know this thread is a little aged, but thought I would reply if anyone else has landed on this with similar issues: try a different USB cable (or 3 different ones!)
I had a similar issue with my 500GB G-Drive Slim - it used to connect, but then it just quit one day. I thought I would try the same USB cable I was using for my G-Drive slim to power up my 500GB G-Drive Mini (which I usually hook up with a firewire 800 cable and I know is working properly). Well wouldn't you know, it didn't connect. The power lights showed up on both drives, though. Then I went and grabbed the USB cable that came with the HD and voila! My G-Drive Slim is now connecting and working properly. Not all USB cables are created equally it seems - apparently some just don't provide enough juice to power a hard disk.
Lesson learned - always use the cables (power or other) that came with the device!