First, did you remove the old modem? I take it it was an internal. Is the new one an external? If not and it was an internal, remove the old modem from your network connection all together, and then go to system in the control panel and check and see if it is still there. (I am not familiar with Millenium Edition to know if it was still in system at that time or elsewhere. If not it will be under the newer add/remeove hardware control.
Make sure you have removed all traces of the old modem and then install the new one to Com 3.
I will say this however, I would never use an internal modem if you paid me. Since modem speeds are slower than the serial line they are attached to anyhow so no way you will suffer from the bus vs. com port bandwidth, external is far superior.
1) Most people don't use their onboard com port so it lies dormant while it has to share the same IRQ as an internal modem (3 and 4) which can lead to some conflicts on older machines running on Com 3 while the serial port is on Com 1
2) The status lights on the external are nice to have when trouble shooting connection problems.
3) When you sell the computer (and you will one day), you can keep your modem if you want! You can even put two togehter and multiplex them through a webramp if you have the two phone lines to use.