System: Pentium 166, 32 MB RAM (yes, I know), Windows 98 SE, IE 5.5, 1.5 GB hard drive with 1 GB free, Intel HaM Plus v.90 Modem.

I'm having a difficult time getting a modem to cooperate.  The computer was my grandmother's and after she died my mother took it to use at her vacation house.  It would not connect when I tried to install my mother's dial-up information and I took it back with me to work on it.  I tried replacing it with a different modem, but I didn't have access to the correct drivers for it so I put the original modem back in.
      I have tried to install the drivers repeatedly with inconsistent results.  Twice in a row the hardware wizard would not find the correct files on the CD, but on the third try, it would suddenly recognize them.  Then it actually connected to the internet but was not connecting at full capacity.  It was connecting at 26000, but was very slow to load a web page.  It took, literally, 10 minutes for the home page to load.  Then when I disconnected and rebooted, it recognized the modem as new hardware all over again. 
     I realize it needs more RAM, but I only had SDRAM and it needs EDO DRAM.  The components are the same as when my grandmother used it.  It worked fine for her.  Somehow, it must be related to the modem and/or setting up a new user account, ISP and dial-up networking.  I eliminated unnecessary background programs, and the system resources are 86% free.  The phone line is the same one my mother uses for her primary computer and it connects at the same speed, but with normal results.  I've been trying to get the modem to connect for several days now.  it will either connect at the slow spped, or I'll get this error message:

"Failure to connect to remote computer.  Unable to establish a connection."  

I don't want to format and start over because there are programs she wants to keep and doesn't have the install disks for.  Any suggestions?  (I'd like to blame it on "nicotine poisoning."  My grandmother was a serious chain smoker.  This computer still smells terrible, and she's been dead since Christmas...)

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