There are a couple of possiblities
1. The modem is on a conflicting IRQ - make sure the modem is operating on com 2 or 4, strange but it does matter.
2. Memory management problem - run msconfig and uncheck any entires under the startup tab that are not required. (reboot to test settings)
3. Swap file corrupted - right click my computer and click properties go into the performance tab and change the virtual memory settings make the swap file min to 1.5x the RAM in the computer.
4. check the network settings, right click network neighborhood and verify the network settings, anything in here that is not necessary remove. Last resort remove and reinstall the dialup adapter and TCP/IP for the dial up adapter.
5. video drivers not functioning correctly (sometimes a problem), download and install a fresh copy of the drivers.
6. When was the last scandisk and defrag? (silly question but it sometimes matters)
Do this anyways its preventive maintenance.
There are more fixes let me know if these work.
JDF