internet sharing problem

Without some hands-on mucking about on site, I doubt if I could
guess or come up with a connectivity answer remotely.

You may have to see about getting a now-discontinued *Apple USB*
Modem so as to connect the newer MacBook via 56k to internet.
The item may be available via an online reseller. Not sure if there
are any suitable clones of this product that would work with OS X.

• Apple USB Modem info: http://en.wikipedia.org/wiki/Apple_Modem

One of the issues found when using this product (discontinued Sept '09)
was if it were in proximity to the MagSafe power magnet socket, it may
affect the connection through the Apple USB Modem adversely.

You can search online and see some resellers have old stock on some
sites, or at least find reference to product info and some leads. Some
may want way more than the original $49. retail price for this product,
*Apple USB Modem (MA034Z/A)* = discontinued September 2009.

Look at older Apple AirPort Extreme Base Stations w/ built-in 56k modem.
They were the top model orb-shaped AEBS that also can support wireless
printers via its USB port; these are some years out of date but still are
available at times. Sometimes they appear at thrift stores, inexpensively.
I've bought two with accessories and power adapters, for $5. and $12.
Plus, have two others I'd bought direct from Apple online, retail. They work.

Other USB 56k modems are available, but whether or not they'd work as
well as the original discontinued Apple USB modem (a software modem)
would be another matter. I've read a bit about them online. And the older
USB modems that are stand-alone products may not function with newer
Mac hardware. This is an area I have no experience in; & have kept a new
spare AEBS (orb model) to allow some compatibility across the board.

The older AEBS with 56k modem built-in supports wireless internet from dial
up; it also had a curious ability to support dial home to your faster networks if
you were away from home & didn't mind phone tolls. Or make private network.
Not sure if any later model AEBS included the 56k built-in modem, after 2005.
The costs of these have come down, especially from private sellers, recently.

If you can get a fair deal on ADSL internet over phone line in your areas,
the increase in speed and no interference with your telephone use (there
is a filter module, for a telephone on digital subscriber lines you'd use) it
is a great leap forward. I've used super-slow dialup, medium slow (24k)
and various speeds of ADSL. Some DSL can be better than cable. There
are about three kinds of DSL; depending on what's available, best o' luck.

If you are using an Ethernet cable to share internet, you may have to
resort to attempting to connect the computers differently; does each
one have an AirPort card? (One computer could supply a signal to the
other one, wirelessly, while getting connection via dialup.) I like my old
AEBS units, since these can support wired and wireless simultaneously,
from cable/dsl + 56k dial-up; and can be used as wireless repeaters.

The model AirPort Extreme (orb) with the better features and no longer
in production, with 56k dial-up, was the AirPort Extreme M8799LL/A.

Hopefully you can try and use a different connectivity option or protocol
and get the MacBook to work online, too. Some people where I am go to
a library or other free access point for their faster internet and suffer with
slow or no internet where they live. Internet is costly & slow here.

There are several settings, some quite different in the newer & older OS X;
I am not currently familiar with their control panels and changes over time.
Even some FireWall port setting may affect Ethernet connections adversely.
And to choose in Network settings to use Ethernet, and drag it to first position
in the panel and also check all related system preference panels is an idea.

Sorry I don't have a 'local answer' to the question you pose at this time.
Good luck & happy computing! 🙂