Since pings are not needed for internet connections, some providers drop them and save the bandwidth for the real work. This can really upset those that used that.
As to the other issues I can't guess what it is given the clues so far but look at your settings on the modem router and see if the PC you want to reach is in the DMZ entry.
What's the DMZ entry? It's in the router manual and explained online so let's hope that will let it work. There are also issues as folk firewall their machine. This is an area your IT skills matter.
Bob
Hi CNET peoples,
Strange problem here, here is the history.
I have Time Warner / Roadrunner internet at my home. I was using a Linksys modem router for the internet and it wasn't the best of modems, it would lock up, I would have no internet until I power cycled the modem. PCAnywhere would work, I could connect to my home computer when I was away from home. I switched back to the Time Warner rented modem and yay, I have internet now but I can't connect to my computer via PCAnywhere. I have already done the pin hole in the router - a Linksys WRT54GS - and still PC Anywhere does not work. I can't even connect to my computer using my internal IP when I have my laptop connected. I have asked my friends to ping my external and they can't it always returns the error message of 4 packets lost 100% data loss. I have called Time Warner and all they say is "Can you connect to the internet? Yes? Then our job is done, contact your IT person for help". This makes no sense, on the other Linksys modem router PC Anywhere and pinging worked, but not on this set up. I have unplugged the modem, router, all computers for a day and powered everything back up, no change. I have already done the router reset, set up the pin hole again and no change.
Does anyone have any ideas?

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic