Thank you, MEB for your reply!
I needed some time to follow on your comments/suggestions.
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MEB
"The computer's modem uses Lucent 1648 technology/V.90. "

"1 Click the My Computer icon on your desktop.
2 Click Control Panel.
3Click Modems.
4 Click the Diagnostics tab.
5 Select COM3.
6 Click More Info."

BAP
Control Panel via My Computer does not show the option for Modems. To do
what you
suggested, I had to go to Settings/Control Panel/Modems.
The Diagnostic tab shows: Com1: Std 1200 bps Modem, Com3: Lucent Win Modem
and Com4:
HSP56 Modem.
'More Info' on Com3 comes back with ‘Could not open port”,
'Port info' comes back with 'Com3 Higher Speed No response.'
Lucent Modem Identifier - WDM- Modem\Lucent_WDM_DF

The following was not shown:
"Specifications:"
"Lucent 1648 technology/V.90 compatible data/fax Modem ?? modem (REN 0.7)"
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MEB
A couple of issues:
First:
You start by showing three modems, a HSP56, HSP56 VVDM Device (PCtel),
Lucent Win
Modem and Standard 1200bps Modem.
Do you have all three of these modems installed?

BAP
I have, yet, to open the case to see if I could identify the presence of any
of them, other than the
PCI card where the Phone line is plugged in, currently.
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MEB
Per Belarc, you have a HSP56, HSP56 VVDM Device (Pctel) and a Standard
1200bps Modem. If any of these is not actually installed/present, you will
have conflicts. What ports and IRQs were shown in Belarc for these modems?
Before proceeding below, please advise the group of the actual IRQs and
addresses being used by each of these devices.

BAP
Belark does not show any IRQs. To see them, I had to go to
Start/Programs/Accessories/System
Tools/Information/ Hardware Resources/IRQ. There, the only obvious IRQs were
IRQ4 for COM1 and IRQ9 for both, RealTek-Fast Ethernet and HSP56. No other
IRQs appeared to be
related to the other Modems. I did notice that IRQ9 is shared by 8 other
unrelated items.
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MEB
Your comport and modem for Netzero should be within the first four standard
port ranges [I say this because of prior issues when I used Netzero, setup
issues, and disconnect issues]. If possible, either reassign the comports in
your BIOS/CMOS or change the cards and connections around, if
not, well if it worked before try it with the below.
System Information/Components/Modem shows your desired modem on Com0. It
also shows you only have two modems.

SECOND, AND THE IMPORTANT ISSUE:
Both AOL and Netzero setup proxy services/servers which attach to and
control the specific device/modem, and the Internet service [Internet
access]. AOL has already claimed the desired modem and setup its
proxy/server/service. You should be able to verify this in the Network
display with its WAN adapter attached to the modem.
If your not using AOL for the Internet access, then go into
modem/connection setup in AOL and *use* the local network [already
established connection NOT a modem, a DO NOT DIAL connection] and let Netzero
use the modem since this is the
new controller proxy/server that you will need. AOL should then connect
through the Netzero service, though it may take some additional tweaks.

BAP
Since I do not use that Computer for AOL, I uninstalled that ISP and found a
NetZero Wizard application, that had been installed with the NetZero
software, and executed it to search for possible problems and the identity of
a Modem.
It came back with HSP56, as the only option.
I was then able to, at least, get a dial tone and dial-up the numbers shown
for my zone. However, for some reason, none of the numbers selected could log
on, as a busy signal could be heard from each. Dialing those numbers on my
phone showed them be open for communication.
On my next trial, from the Netzero help files, I followed the suggestion to
double click on My Computer, then click on the Netzero icon, followed by
selecting the Files Tab and clicking on Delete. From what I could gather,
that would have been a way of disabling the high speed communication setting,
which might have been interfering and not allow the call to go thru.
Surprisingly, the connection was made, although on the first try, a fatal
error occurred with my Explorer and I had no choice, but to shutdown and
restart. That led to system to scan the Hard Disk for errors. After that, it
seemed that a connection could be made, without errors.
At this point, I am able to connect, but am sort of disappointed that the
claim of the fastest dial-up speed has not lived up to expectations. The
speed is not much faster, if at all, than the speed of AOL.
Again, thank you for your help in pointing  the way to get things going.  
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