Regarding the livecd: If it doesn't boot with a working mouse and keyboard, what happens if you boot without either connected and then plug in? USB devices are hotpluggable, so this should load the necessary modules.

I booted up with the live CD with keyboard. Wnen the first menu appeared, I pressed <return> which implemented "live CD", unplugged the keyboard, and allowed it to boot up. Note: the CD DID recognize the keyboard until AFTER I invoked "live CD".
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I don't know what your problem may be but I just installed Debian using Logitec mk300 combination & had no problems with it.

You don't say which flavor of Debian.
A wheezy ia64 live CD recognizes my keyboard+mouse; Lenny recognizes my keyboard+mouse; the wheezy amd64 live CD initially recognizes my keyboard until I boot up wheezy. What is different about wheezy amd64?

Wheezy amd64

I've not seen an ia64 livecd and not sure your hardware is ia64. You haven't specified whether Lenny was i386 or amd64...

The error messages look like the result of faulty hardware. I'm not sure why this is being exposed with a newer kernel and not with the 2.6.x kernel - maybe the earlier ehci_hcd module does not attempt to claim that device...? I would suggest disabling the USB 2.0 controller from your BIOS setup (this will leave USB 1.1 enabled) and try the wheezy amd64 livecd again - exactly as before.

The BIOS will allow me to disable USB 3.0/2.0 which goes thru the PCI Express bus which goes to the AMD 970 (Northbridge?). That still allows 2.0/1.1 which goes to the AMD SB950 (Southbridge?). The only diagnostic difference that I could see was that the address number that it could not connect to changed.

Incidentally, I played with the "enable PS2 emulation" in the BIOS. Although it has no effect on AMD64 Oldstable, disabling the emulation means that the keyboard is not recognized when I start the debian-live-7.5.0-amd64. Apparently the CD gets to the keyboard via the BIOS until it boots up 7.5.0. In other words, I cannot initiate the live 7.5.0 unless the PS2 emulation is enabled.

I can borrow a PS2 keyboard from a friend for a few days. That will allow me to communicate w/o USB.
What diagnostics do you need: lsub, lsmod, ?

The ps/2 thing is usually the same as the usb "legacy emulation". Disabling USB 3.0 is ok, but it probably won't help unless you can disable USB 2.0.

If you can't do that, then unfortunately I might have to suggest that you build a new kernel with USB 2.0 (and 3.0) disabled as a precaution. It's a pain in the rear, but it's what you have to do to troubleshoot stuff (unless someone else turns up with a solution). The problem with blacklisting modules is that it doesn't work well for USB as the modules you want to prevent loading can still get loaded when devices are plugged out/in or when other modules request them.

You should do all of your testing by booting without any USB devices attached. Then plug in just the keyboard/mouse and see if they start to work normally. If you still get the same errors in dmesg, then you really will have to move onto kernel building.

Before you do any of that, once you have the ps/2 keyboard, you could try the latest kernel from backports (probably 3.14, not sure) - who knows the 'problem' might have been resolved? (it's worth a try).

I anticipated kernel problems when I started this thread.
H. L. Menken: "For every difficult, complicated problem, there is a simple, elegant solution that won't work."
With a PS2 keyboard (the motherboard only has one PS2 socket; no mouse): debian-live-7.5.0-amd64
At least with a PS2 keyboard I can communicate with the OS.
When I tried to plug in a USB adapter for an SD chip, I got the same error message: "Cannot enumerate ..."

That doesn't look like lsmod output...

If you're getting the same error from other devices then probably the kernel is the next step.

Try the latest backports kernel first.

Pardon me: That was lsusb, not lsmod. Lsmod output ran off the page. I hand copied the lsusb from the live CD output.
I am a pretty good C programmer. However, I have never delved into the kernel before. Presumably, I need to start by downloading the wheezy module that generates the message, "Cannot enumerate"; compile that as a stand-alone program from command line in root. Once I have duplicated the errant behavior, compare the differences with the similar squeeze module source code, which apparently works.

I wouldn't even recognize the appropriate source code if it walked up and bit me. Could you point me in the right direction?

Trying to find the problem in the actual kernel module source would actually be very time consuming and probably not solve your problem anyway. You may be working on fixing something which someone else has already resolved in a later kernel.

You should try the backports 3.14 kernel first. Install initramfs-tools from backports first/at the same time.

If that doesn't help, get the source for the 3.14 kernel from testing/unstable source repo, completely remove USB 2.0 and 3.0 support and build and install it (don't just install a binary kernel package from testing/unstable). Make sure to build an initrd (if you build your kernel the Debian way, this should be done for you).

I tried the backports route. I probably didn't do it correctly. I downloaded the .deb & .udeb packages, and tried to install them using dpkg. Dependency issues reached the ssh package. At that point, I bit the bullet and dist-upgrade first to wheezy and then to jessie. No joy.
The upgrade route has two advantages over loading from an iso: I can still boot up with 6.0.8, and the wheezy and jessy install packages want my NIC firmware loaded. Since the installer does not recognize my USB devices and I don't have a second CDROM drive, providing the installer with the firmware is problematic.

I now have jessie loaded; I am getting the identical error messages as previously; I have a PS2 keyboard working, but no rodent support.

Per suggestion from a friend, I installed a USB card in a PCI slot. According to the Gigabyte users manual, that connects to the Southbridge, as does the USB 2.0/1.1. Identical diagnostics. Fooey and stronger language.

Add backports to /etc/apt/sources.list.
No need to download source packages and use dpkg.