The DSL connection log would be on your modem/router, not on your XP computer.
What country are you in? I know over here in the UK, ADSL microfilters are required to filter out noise on the line (I just noticed the ADSL tag). I would strongly recommend replacing the microfilter and see if this helps before trying anything else.
Failing this, you would be best off speaking to your internet provider who should have the ability to check the logs their end and run line tests to determine the root cause of the problem.
One question, are you connecting to your modem/router wirelessly or with a cable? If wirelessly, try with a cable. If with a cable, are there any other computers in your house/office that you can test with to rule out a problem with an individual computer?