I don't think there are any horrible effects of leaving it on for 8 days.
When i was on dial up, i used to leave my computer on for days at a time too. i never experienced any problems. I would shut off the monitor to save power.
the room with the computer in it was warmer than the other rooms.
Other than that, i had no issues.
By the way, just how big is this file that is going to take 8 days to download? I usually try to reconnect and get a better connection speed if it's going to take more than an hour.