A lower cost alternative to the 3Com device is the Actiontec Dual PC Modem.  It is in the $70 range and you can read about it at:

http://www.cdw.com/shop/products/default.aspx?edc=528453

There are other similar ones from other manufacturers.

Doug
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Sue Wrote:

If there is a router that would work with an analog dial up
connection, I'd love to hear about it, because if necessary, that's the way I could go. But I'm hoping someone would have suggestions as to why the ping might be timing out and what, if anything I can do about it. Again, everything works (in fact no matter how many times I change the configurations) as a network, just no internet connection sharing.

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