Mac ignores My Passport USB drive

Hi, everybody. This problem seems to go a bit beyond the typical “my drive isn’t working” problem. My little 1 TB My Passport drive is having some kind of problem that keeps it from being acknowledged by my Mac when I plug it in. It doesn’t show up on the desktop or in Disk Utility, and my Mac acts like it hasn’t been plugged it at all. It does spin up, however, just like normal, but nothing else happens — including no activity from the indicator light. I’ve plugged it into multiple Macs with different USB cables, all with the same result.

I had hoped to break open the drive and put the SATA into a new enclosure, but unfortunately WD is using some proprietary logic board that’s actually part of the hard drive itself, so this is impossible. Are there any other solutions to get this drive readable again? (It actually showed up briefly on my Mac last night, but I wasn’t able to copy any files from it before it disappeared again, so I’m hoping the data inside is still intact somehow.)

Thanks in advance for any help you might be able to offer.

One brief follow-up: under rare circumstances (usually when plugging the drive in while it’s raised above desk-level for some reason), I can get the drive to appear. If I try to do anything with it, however, such as examine it with Disk Utility or open it in the Finder, the app using it hangs and then freezes up, refusing even to be force-quit until I physically unplug the drive.