[LATER:] As described under #1 below, I reinstalled LMDE 64 and now it doesn't seem to have any problems at boot from errors caused by looking for partitions that were formerly on the IDE disk. So far, I am able to boot normally. So I will mark this solved again tentatively.
[EVEN LATER:] I really should re-title this issue: "Why does LMDE 64 hate my second IDE hard drive?" The problem of losing the desktop and MintMenu DID recur at the next boot. Why? - I have no idea. I once again get the message during boot: "Mounting local filesystems... mount: special device /dev/sda4 does not exist." (sda4 is my /home partition). When I disconnect the IDE drive, LMDE boots normally. I have seen mention of Debian having problems with mixed SATA and PATA (IDE) drives. I guess this is one of them. I'm speculating that the solution is to change some spec so that LMDE recognizes the IDE drive properly at boot, which I don't know how to do (but will search for a solution in the Debian world). Though I can't imagine why the presence of an IDE drive prevents LMDE from finding /dev/sda4, which is my /home partition. OKAY, my solution was to replace the IDE drive with a SATA drive, probably overdue anyway.
[LATER STILL:] A search on the Debian forums for .ICEauthority (part of the error messages described below) hints that this particular error may have something to do with sound settings. But then, it also turns up the usual 40-acre rabbit warren of side issues, diversions, distractions, and airy speculation. Linux is wonderful once everything's running smoothly.
1. Upon first boot after repartitioning the second (IDE) drive in this PC I had the error messages described below once again (.ICEauthority...etc.). Hm, an external USB hard drive was attached and running, but I don't think that could have caused the problem.
Anyway, I booted again and the desktop and MintMenu came up, but all my settings re monitors, desktop icons, etc. were gone - looked like it did after a first boot of a freshly installed LMDE with the old, un-re-partitioned/formatted IDE drive.
I noticed during startup a message: "Mounting local filesystems... mount: special device /dev/sda4 does not exist." I reckon LMDE was looking for a partition that formerly existed on the IDE drive, before I repartitioned and reformatted it as described in the "NOTE:" below. Wonder if that's what threw LMDE off balance. As we speak, I'm re-installing LMDE fresh now that the IDE drive is in fresh clean condition with no old Linux partitions anymore. Hm, but given success described under "NOTE:", I'm confused. Anyway, will proceed with the reinstall.
2. [NOTE: This issue was SOLVED step by step. First by disconnecting the IDE (PATA) hard drive during installation of LMDE 64. The installation thereafter went fine, and on re-boot after install, the MintMenu and desktop were loaded properly. However, when the IDE drive was re-connected and the computer was re-booted, the problem described below appeared - boot disk not detected, no MintMenu, no desktop. The solution was to back up the IDE drive, repartition it with a single NTFS partition (it is my Windows/Linux data disk), and format it. After I did that, I was able to boot into the LMDE 64 desktop normally, with no error messages and the MintMenu nicely in place. Hurrah.]
I received the following messages in this sequence after installing LMDE 64 201012 on a home-built PC with Biostar 790GA A2+ motherboard, AMD Phenom 9850 4-core, and 4 GB RAM:
Could not update .ICEauthority file /home/runbei/.ICEauthority
There is a problem with the configuration server (/usr/lib/libgconf-2-4/gconf-sanity-check2 exited with status 256)
The panel encountered a problem while loading "0AFIID:6x10ME_MintMenu". Do you want to delete the applet from your configuration?
(Problem recurs on reboot whether I choose Delete or Don't Delete.)
Nautilus could not create the following required folders: /home/runbei/Desktop, /home/runbei/.nautilus. Please create these folders, or set permissions such that nautilus can create them.
Obviously, there's no MintMenu or Desktop at install. I'll be trying LMDE 32 on the same machine. It installed normally on my laptop, a ThinkPad X32, although (like all Debian-based distros), suspend to RAM does not work - it leaves the backlight on and freezes on resume. (FWIW, OpenSUSE and Scientific Linux both handle suspend flawlessly.)
Still looking for a very stable rolling distro to use on that machine. It clearly isn't Debian (too techie for me), Mepis (too much manual mangling required to set up Nvidia drivers, etc., with poor documentation), or LMDE 64 (yet). But given what's been done with Mint in the past I'm highly optimistic that one of these days I'll have LMDE 64 running smoothly (tracking Stable) with Windows in Virtualbox and, $ allowing, 8 GB of RAM.