First of all, thanks to those of you who responded, both here and via e-mail.
The tips didn't pan out, but it was good hearing from you.

Now, following up to my earlier post:
[...]
: Disk controller:  Acculogic sIDE-3 2 hard/2 floppy IDE controller
:   Jumpers:  All defaulted (shown as *):  
:     Normal IRQ*/delayed IRQ     Primary*/secondary floppy address
:     Single*/dual speed floppy   Primary*/secondary IDE address
:     Precomp = 125ns*/187 ns     IOCHRDY not driven*/IDE drive controls IOCHRDY
[...]
: Other cards:  (didn't check brand) 2 Serial/1 Parallel adapter
: 	      Logitech Bus Mouse adapter
: 	      Roland MPU-401-compatible MIDI interface 
: 		Configured with default IRQ 2, mem address 0330

I opened up the box and removed all the "other cards" above.  No help there.
Then, not having anything better to try, I changed Normal IRQ to Delayed
IRQ on the disk controller (didn't make any difference) and IOCHRDY_not_
driven to IDE_drive_controls_IOCHRDY (also had no effect).  So I put 
everything back to the way it was and re-installed the cards.

I then unplugged the floppy drive cable from the disk controller.  Voila!,
the PC booted from power up, although it seemed to take several seconds 
before the first access to the hard disk.  Plug the floppy cable back
to the controller and the original (non-boot) behavior returns.

O.K., with this additional information, does anyone in netland have any 
words of wisdom for what's going on and how I should deal with it?