My Passport Essential not recognized on XP PC

I recently purchased a WD My Passport Essential drive to back up my documents, photos, and music to after my computer began to swiftly signal the end of its life. I quickly backed up all of my data by simply copy/pasting everything from the hard drive to the external drive. I’m painfully new at this sort of thing, so I realize that I may have made a critical mistake in doing so. Now that I’ve plugged the drive into another, older laptop that I’m using until my new system arrives, the Passport does not show up in “My Computer” when I plug it in. I was browsing through some forums in search of an answer, and read somewhere that the device is supposed to vibrate when it’s plugged in - it doesn’t. The white light on the side is blinking slowly, and it shows up in Device Manager as a hard drive, but it does not show up in Computer Management. I realize now, of course, that I should have formatted the drive before I just started putting things on it, but the info is on there now. I’m not positive if I can still retrieve my data from the broken laptop, so I don’t want to reformat the drive and risk losing everything. Is there any way to retrieve the data from the drive? The system I took the info. from was running Windows Vista 32 bit, the system I’m currently using is on XP Professional. Any help would be greatly appreciated!

Is the XP up to date with SP3 and other critical updates? Make sure the power adapter is plugged directly in the wall and not a power strip. Don’t use a hub on the USB connection.