If you look at the female pins of where the modem line plugs into the PCMCIA card you'll probably find that they are weak and have given way (don't pop miraculously back into position when you pull the plug out. My Dell 3500's XIRCOM modem/network card had this flaw and the problem was there on the Network cable's port also.
It was out of warranty - but I just got a broken match and wedged it in behind the pins in order to hold them in place. So far no further problems. I'd suspect that your pins have crossed over perhaps (they are quite long, thin, puny and unsupported. That's usually why all sorts of miniport outlets give trouble (Walkmans, trannie radios, PCMCIA and TV cards etc). Maybe they just build them too fragile on purpose as a means of achieving planned obsolescence. However any external cable will also have all sorts of leverage on it from weight of the cable, attached transformers and batt chargers etc - and so will givge up the ghost eventually. And of course portable devices are always being pulled out and re-attached......
Currently looking as though I will have to pull my Dell Inspiron 3500 Notebook to pieces again because the sound outlet plug innards have quit in similar fashion. Wouldn't buy a Dell again because it's now twice bitten.....