Windows can't read the filesystem used by OS X. You should not get a drive letter when plugging it into Windows. Things like CDs and flash drives work because they use different filesystems (at least I think OS X plays nice and uses a more widely use filesystem for flash drives).
There are, however, some programs out there that can make this work in a roundabout way, allowing you to "mount" the drive in Windows using the program as the middle man. You could use one of these to determine if the drive is working, using the Windows computer. Unfortunately, I don't know the name of any such programs off the top of my head. You can probably find one in 30 seconds of Googling.
nao1120 :
You need to use another MAC that can read the drive HFS file system.
It's actually HFS+. Could be an important distinction when looking at freeware to mount the drive (freeware often has crap compatibility, wouldn't be surprised to see one that supports HFS but not HFS+).
I don't really get why drives brick like that, You would think they would just be terribly loud, and thus allow you to notice this/back up etc.
That might happen if the bearing went out, but this pretty much never happens. Hard drives can fail in many interesting ways, and pretty much all of them are silent and have no warning. One of the most common, and most insidious, is the "head crash." This occurs when the drive head (the bit that reads/writes data from the drive) comes into contact with the platter. Since the platters move at incredibly high speed, this causes the head to literally gouge out a track on the platter, destroying the drive forever. This is why you're not supposed to move computers while they're on, by the way. Laptops drives are likely designed to tolerate more movement (I've never actually looked into it).