Hi, again, luya56...

A simple thought re: your problem...

What I wonder is whether or not you may have performed an update of your XP Home installation ?

Especially an update that involved installing Windows XP Service Pack 2.
(XP Service Pack 2 is a bit notorious as it includes a 'built-in' firewall that is enabled as default. Best to disable it.)

Perhaps, because of your relatively small bandwidth capacity, you had avoided Microsoft updates in the past but now you have done the SP2 update ???

I am also a bit confused as you state that you are using the Conexant Soft K56 Modem AND another Modem/Router, the BT Voyager...
You are not using both. Perhaps the Conexant is for a FAX line or something ?

And, a little later... Right- I checked the BT Voyager 105... It's an ADSL modem router so, there goes all that sympathy for you re: your slow dial-up connection...

But, this only reinforces my thought that it is possible that you did do the XP SP2 update fairly recently and the SP2 firewall may be the culprit !