It doesn't sound like a hardware problem to me. A PCI modem and a serial modem work very differently as far as your motherboard is concerned.
It's possible that you may be infected with a virus or spyware. -- I have seen computers that do strange things only once connected to the 'Net, and usually spyware is the cause.
Can you clarify what 'freezes up' means to you? Does the mouse still move? Does the keyboard still work? - try hitting Numlock & check that the LED still switches off and on.