Two days to switch the power off and on? This could be a long one.
Since the other system is working fine it's less likely the DSL modem is responsible, but what brand/model? What was the last time it was powered off? (Be sure to catch the router as well.) Again, it's unlikely to be the cause, but a reset is fast and free.
Have you tried web browsing with your bt client stopped? Which bt client?
What else have you tried to fix the problems?
Let us know.