To change the number of rings before Dial up Networking Server answers:

Find the INF file for the modem in the \WINDOWS\INF directory. The filename will begin with "mdm" and end with characters desciptive of the manufacturer, ie. "supra" for Supra Express modem.
Make a copy of this file.
Edit this file with notepad and look for a string "HKR, Answer, 1,, "ATA<cr>".
Change to HKR, Answer, 1,, "None".
A few lines up from this should be the line HKR, Monitor, 1,, "ATS0=0<cr>" Change the value of the S0 register to the number of rings you would like to have the modem answer on.
Remove the modem by using the Control panel | System | Device Manager.
Reinstall the modem using the REFRESH Button.
This should install the modem using the updated INF file.