USB Mass Storage Device not Assigning a Letter

I have Windows ME on an HP laptop with its own hard drive. I have tried
to attach 2 USB mass storage devices. One is a hard drive enclosure
with a 3.5" (desktop) hard drive & the other is a hard drive enclosure
with a 2.5" (laptop) drive. When I plug the 2.5" enclosure in and boot
the computer, it recognizes the drive just fine & assigns it a drive
letter. When I plug the 3.5" enclosure into the same USB port & boot
the computer, Windows recognizes it as new hardware, & it is recognized
as a device that needs to be stopped before disconnection from the
computer, but no drive letter is assigned.

The 2.5" enclosure is powered through the laptop, but the 3.5" has its
own power supply & on/off switch. When I turn on the on/off switch,
green Power light & the red Read/Write light both come on, then, after
a few seconds, the green Power light goes off. I tried setting the
jumper settings as "slave" and as "Master or single drive" with no
change in result. I also made sure the cable was properly plugged into
the drive.

The 3.5" hard drive is a Seagate, 30GB, used. I tried the 3.5" setup on
another laptop. It was a much newer Dell with WinXP and the exact same
thing happened on that computer (recognized the hardware, didn't assign
letter). I don't have a desktop computer or anyplace else to test this
drive. Could the drive or enclosure be bad?

Thank you for any help you can provide. If any more specs are needed,
I'll be happy to provide them ASAP!