How do you know that the packets are being dropped between the router and the modem? DSL is notorious for dropping packets when the line quality is low.
You can't connect your modem directly to your computer to check because it's integrated... but if you have another DSL modem, I'd try connecting it directly to a computer. If it works fine, the router is the culprit for sure.
as a side note: most ISPs can run a line quality check. Calling up your provider and asking them to run a check might be helpful.