The COM3 should not be a problem, that is where mine installs.
I assume you are talking about an internal WinModem. The setup configuration files for the modem define which ports the adapter can work on, and the Plug and Play logic picks one. Most likely there are two serial ports on the system board taking the first two COM ports, so COM3 is the next in sequence. Some WinModems will only work on COM5 and their configuration files will not allow them to be placed on COM3. So there is the very small remote possibility you have the wrong drivers for the modem.
But otherwise, the drivers and Windows don't really care which COM# a modem is assigned. It should work OK, as long as there are no conflicts showing for the device in Device Manager.
More likely it could be something as simple as the phone line being plugged into the wrong hole. Most modem cards it does not make a difference, but on some it does. Normally you would plug the phone line into the bottom plug. But the one I have is different in that it requires the phone line to be plugged into the top plug. (Took me a day to figure that one out.)
Start by going to Control Panel, Modem tab. Then in Modems Properties click on Diagnostics tab. Then select the COM3 by clicking on it. It should show the modem name beside COM3. With COM3 selected, click on the More Infor.. button. This should show you the response of AT commands to the modem. If this works OK then the modem is OK and the drivers are correctly installed.
An error message here, indicates there may be a problem with the modem or the wrong drivers are installed.