It might have been the Pentium II with something like 64 Mb. RAM.
I had an AMD K6@ 300MHz. with 64 Mb. RAM on Win 95, similar to a Pentium II of the era, and the speed issues improved greatly when I increased the RAM amount to 256 Mb.
The satellite dial-up system sounds like the Hughes Satellite system.
I think that was the only satellite system available at the time.
That system is now Direct TV Satellite Internet, but it is and was Not Slow.
The dial-up side is not used for downloading, only for page and file requests since there is no direct way for a user to ask a satellite for a page.
The satellite is what downloads the pages and files.
The user requests a page though the dial-up connection to the Hughes server switchboard via the telephone line. The switchboard passes the request to the server computer,
and the server computer beams the data almost instantly to the high speed satellite hovering high above the Earth which then bounces the data back to earth and is picked up by the receiver dish and then whisked straight to the Pentium II 64Mb. RAM desktop system.
The satellites in use, then and now, are telecom satellites with ultra high data transmission rates, the same satellites as those which carry the bulk of international phone calls, The Internet, live video, The OSCARS, The Superbowl, and Direct TV or Dish On Demand.
EDIT: That computer might have had a floggy configuration or virus/malware. Back then was the era of mass drive-by infections.