Temporary Respite till you remove the Dial up modem
Open Internet Options .by Right clicking on the Internet Explorer Icon on the Top of the Start list and choose Properties up and click the Connections tab
Change the setting to Never dial a connection then click on the Apply then the OK button to save and exit this page
Should be a bit more stable now?

Question, Is the Modem an external or an internal unit?
The external unit should be unplugged completely and B) The Software ininstalled ...Internal unit is basically removing the card When switched off (May need assistance to remove it from the Tower ?) Then an uninstall of the Modem software take 5 minutes Tops