In our High-Tec world a very unusual question. What you need to do is, find a provider where you can still access the net on a text only basis.
Lived in India for quiet some time and there is still a Standard Account available for simple browsing, also PPRuNe is accessible this way.
But under no circumstances is any access to graphical display possible.
The problem is more on the modem side. Your system will not allow for now-a-days transfer speed. 9600 baud is a very realistic one, that is even slower than most telefaxes work on.
With text only display it still will be reasonably fast, it will still beat any 33xxx speed without V90 compression.
A better solution for this machine would be to work as a dedicated print server etc. will still do a nice job....I am running a 386 with win 3.1 doing backups and printjobs with it....also i am told it is not required, well, after 21 years with computers, i know it speeds my process up and I am still happy.....
AND....it still starts faster than my P3-500 with all the phantastic bits and pieces....