Limit to external hard drives on my laptop?

Is there a limit to the number of hard drives a laptop (or any computer) will easily PnP with until it ceases to easily add a newly added external hard drive, i.e., starts giving driver install failed errors?

I'm about to wipe my laptop anyway so this will become a moot point but I'd like to know anyway.

I own a:
Dell Studio XPS 1645
Windows 7 SP1 64-bit (home premium)

I've attached printers, external hard drives (Seagate, Western Digital, LaCie), printers, USB hubs (2) simultaneously, a laptop fan, mouse, all without too much of a problem. . .ever.
Until recently (and no, I don't know what I might have installed). But nonetheless, I've been trying to get my computer to recognize several different HD's that have never been attached to it before and 2 new ones, and it cannot install and attach to any of them. I look on the manufacturer's website and they say that the hard drive doesn't need a driver (Seagate and Western Digital). I know that the hard drives are functional as they work on other W7 and XP machines.

I've already gone to DevMgr --> DiskMgmt and attempted to assign a different drive letter - that's not the issue as the drive doesn't show up in Disk Management at all. It does show up in the Control Panel's Devices but is not useable.

I've tried Eraseus Partition Manager just to see I could see it. Not there.
I've switched cables and power cords.
I've checked for additional updates.
Each time I do something, before I do it, I safely unplug everything, i.e., use safe remove (so the laptop "knows" something is there as it shows up in the list of things to remove), unplug the usb cable from the laptop, unplug it from the ext hd, unplug the power cord from the ext hd, shut down the computer. And start again.
I've uninstalled usb from device manager. No go.

There has got to be something so silly that I'm overlooking - I just can't see it anymore.

I'd appreciate your help.

Lost in the forest with a broken compass.