Hey, I have been doing internet technical support for over 100 different ISP's for a couple of years.. I have seen this way too many times.
Disconnections are caused almost 99% by the phone line or the modem. If it is a phone line issue, answer these questions to find out:
1) Is your phone cord long? (over 6 feet)
2) Do you have call waiting on your phone line?
3) Do you have any splitters on the phone line?
4) Does your phone line go through a phone line surge protector?
5) Does your phone line go through a fax machine?
6) Do you ever hear echo's or static on your phone line while talking?
7) How old are the lines in the place you live?
8) Do you have a cordless phone with a dead or low battery hooked up to the phone line?, if so, disconnect it from the phone line.
9) Has there been any electrical storms in your area lately?
And.. if it is a modem issue:
1) How old is the modem?
2) Set the maximum speed to the modem to 57600
3) Set the flow control of the modem to software
4) Try lowering the fifo buffers
5) Is it v.90, if so, try using an init string to disable v.90
6) Get the exact model of your modem and search for some init strings for it
7) How long has it been since the drivers have been updated, your second computer could be working fine because it may be more compatible with the modems that the ISP are using, drivers could solve this issue.
8) Is the modem a Windows Modem?, if you have a winmodem on a slower computer, it can cause disconnections.
What ISP are you with.. I may work for them =)
Hope this helps,
Jayme