The ping is showing consistent packet loss, and the router is pointing to an issue with the connection between your router (on the first hop) and your modem (on the 2nd). Are you able connect directly to the modem via ethernet and perform the same tests again for comparison?
When I log into the admin page of my router, I go to Tools and there is a network ping test which allows me to enter a URL or IP address, and my router then sends a ping to that host and tells me if it is able to get through. If you could find this, it would tell you if the router is getting the proper signal and able to send/receive data from the internet.
When you hook up the laptop to the router, do you know if it is connecting? If you are using Windows XP it should tell you in the system tray (bottom right) something like "Wireless Connection | Status: Connected". Otherwise, you can check by going to 'Network' from the Control Panel. Knowing this is a good point begin to troubleshoot your issue.
Sorry, I wasn't very clear. To access "CMD" click start > run > and type cmd in the "Open:" field. This will bring you to the command prompt (like MSDOS). Then try the commands I put above, ping and traceroute. You can copy from CMD by right-clicking the screen and choosing "Mark". This allows you to highlight text. Then press enter to copy the highlighted text so you can paste back here.
Looks like the first hop in your traceroute shows trouble. Using a router? If so -- what kind? using wireless? If not using a router -- post up your modem stats (http://192.168.100.1/) and/or call your ISP and let em know about your latency issues!
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