Which Internet provider is it?
Do you know the model of the ADSL modem you use?
Is it affecting eveything like web, mail etc.?
Are you using wireless to connect?
Very hard to troubleshoot from afar, but might be worth having a word with your ISP if they have a support line this time of the night as there could be issues at their end, on the line or even at the phone company (depending where you live).
Another thing thats worth doing is removing everything from the line except the computer and trying that way. Sometimes other stuff can interfere.
Trev