Update:

Okay, got around to testing my printer and try the suggestions to keep
if from going beserk on power up (on the parallel port, not from
powering up the printer). Changing the parallel port modes in BIOS did
not help. Disable the parallel port in BIOS did not help. So I suspect
that the NF7-S motherboard doesn't keep the signal pins low or
disconnected when first powered up which results in the printer getting
a scrambled mess of signals which it tries to interpret as commands.

I switched the printer from the parallel port to the USB port. The
printer supports both. The printer is slower than the bandwidth for the
parallel port so I saw no need to throw away a perfectly good and
capable port - until now. It took a couple uninstalls of old HP
software, deleting printers, and reboots to get a new driver install to
work (it first reported it couldn't find the printer until I had it do a
rescan) and now the printer works. It no longer goes beserk on powering
up the system unit and the test and calibration pages have printed okay.

So the problem went away (actually it got masked) by moving the printer
from the parallel port to the USB port.