Again, this failure to properly detect V.90 is probably NOT limited to Compaq PC's. You are using a 56K modem and the software inside your modem needs updated . Your computer has been idle for 20 minutes or more, causing the system to automatically disconnect. Telephone answering machines on the same line as your PC can cause havoc. Try uplugging yours if you have one.
Extension phones on the same line have been know to cause problems.
Call Waiting , if you have it, MUST be disbled while you are on-line. The problem is simple. Every program you have that connects to the net, has a setting telling it which dial-up networking account to use. In the third case, this is normal. Either don't leave you computer online for long periods of time doing nothing or set your email to check for mail every few minutes.