The Voice,
2. The lappy doesn't have a drama at all and maintains the connection (unless in really bad weather, then it may become unstable)
That sounds like a hint that there is possibly something wrong with the telephone line itself. Rain should not be a problem unless there is a part of the telephone wire exposed to the elements due to age or a cut in the line. I would first have the Telco check that out. (Do you get static on your phone line when it rains?)
If your desktop has a WinModem in it, I would replace it no matter what is found wrong with your phone lines. WinModems are junk and their only good use is as a key chain.
I would look at a USRobotics Performance Pro Modem or external USB Modem.
Performance Pro Modem:
USB 2.0 External Modem:
Take Care,
Richard