Well, it was a wild guess.

But perhaps not *too* wild -- see below.
It was a clean, default KDE install from the DVD image held on disk. So DISPLAYMANAGER=kdm, DESKTOP=KDE4. The problem was first observed on a completely new account, created as a part of the install process. I've just double-checked it, setting up a new test account -- same trouble.
However, switching quickly to Ctrl-Alt-F12 while waiting for the password field to get focus, I note that the end of the delay appears to coincide with all disks being re-mounted! And /var/log/syslog shows the test appended at the end of this post.
The "no IPv6 routers present" line is the first one I see on the scrolling display on F12. It's preceded by a six second gap, -- the login ID was entered during that gap (it took me less than 6 seconds to type "test" and hit Ctrl-Alt-F12). The cursor starts blinking in the password field just after the re-mounts.
(Incidentally, another oddity... The X session is sometimes on F7 and sometimes on F1; when on F7, F1 shows absolutely nothing -- blank screen -- one has to go to F2 for console login.)
May 26 10:25:38 Athlon kernel: [ 24.079515] ppdev0: no associated port!
May 26 10:25:44 Athlon kernel: [ 29.890016] eth0: no IPv6 routers present
May 26 10:25:49 Athlon kernel: [ 34.720033] ata4.00: exception Emask 0x0 SAct 0x0 SErr 0x0 action 0x6 frozen
May 26 10:25:49 Athlon kernel: [ 34.720038] ata4.00: failed command: SET FEATURES
May 26 10:25:49 Athlon kernel: [ 34.720043] ata4.00: cmd ef/c2:00:00:00:00/00:00:00:00:00/40 tag 0
May 26 10:25:49 Athlon kernel: [ 34.720044] res 40/00:fe:00:00:00/00:00:00:00:00/40 Emask 0x4 (timeout)
May 26 10:25:49 Athlon kernel: [ 34.720047] ata4.00: status: { DRDY }
May 26 10:25:49 Athlon kernel: [ 34.720052] ata4: hard resetting link
May 26 10:25:50 Athlon kernel: [ 35.025012] ata4: SATA link up 1.5 Gbps (SStatus 113 SControl 300)
May 26 10:25:50 Athlon kernel: [ 35.028072] ata4.00: configured for UDMA/133
May 26 10:25:50 Athlon kernel: [ 35.028084] ata4: EH complete
May 26 10:25:50 Athlon kernel: [ 35.043562] ata4.00: configured for UDMA/133
May 26 10:25:50 Athlon kernel: [ 35.043565] ata4: EH complete
May 26 10:25:50 Athlon hddtemp[1312]: Starting hard disk temperature monitor daemon[ OK ]
May 26 10:25:50 Athlon systemd[1]: Startup finished in 1s 460ms 227us (kernel) + 5s 64ms 844us (initrd) + 28s 773ms 963us (userspace) = 35s 299ms 34us.
May 26 10:25:50 Athlon kernel: [ 35.404147] EXT4-fs (sda10): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.488811] EXT4-fs (sdb10): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.574073] EXT4-fs (sdb14): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.667704] EXT4-fs (sdb6): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.724203] EXT4-fs (sdb13): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.811978] EXT4-fs (sdb16): re-mounted. Opts: commit=0
May 26 10:25:50 Athlon kernel: [ 35.888520] EXT4-fs (sdb8): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 35.953330] EXT4-fs (sdb1): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.015871] EXT4-fs (sdb15): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.075341] EXT4-fs (sdb5): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.156413] EXT4-fs (sdb12): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.221439] EXT4-fs (sda7): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.302046] EXT4-fs (sdb7): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.369847] EXT4-fs (sdb11): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.417179] EXT4-fs (sda9): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.455380] EXT4-fs (sda8): re-mounted. Opts: commit=0
May 26 10:25:51 Athlon kernel: [ 36.497900] EXT4-fs (sda6): re-mounted. Opts: commit=0
May 26 10:28:31 Athlon acpid: client 937[0:0] has disconnected