Run MSINFO32.EXE and expand the Hardware Resources section. All info is there about what resources the system devices are using. Although some devices share resources some can cause problems. So whatever's the same as the modem is causing this. The sound card is usually on IRQ 5 this may be a place to start. Also you can see if there are available IRQs that the modem may be able to use.
By default the COM ports use the following settings.
COM1,3E8, COM3,2E8 both use IRQ4
COM2,2F8, COM4,3F8 both use IRQ3
As was correctly stated, to free up resources, disable one or both of the com ports from the BIOS. Since the modem's COM3 you would disable COM1. If the modem was COM4 you would disable COM2.
Before modems had jumpers that were used to hard set the port, IRQ and I/O address. If a port was disabled in the BIOS you could jump the modem to use those resources and for sure it would work.
Welcome to plug and pray! The PCI bus will assign devices to use the same resources. Windows sometimes cannot handle this. There won't be any noted conflicts but the system could have all sorts of problems.
Check through your PCI settings in the BIOS. If you're lucky it will allow you to specify slot settings.
Moving the card to another slot is also a way to eliminate this issue.
USR modems can be a bit tough, so take the time to read the help files on the CD.