You could do some more debugging. You have not mentioned your network topology -- is your Windows 7 machine, on which tomcat 6 is running, behind a NAT of some kind? You mentioned multiples machines (the Ubuntu box) so I would assume it is the case, unless you have some exotic scenario where every single machine has a routable, public IP address (I have seen some aDSL providers do this on multiple occasions here, for some reason).
The first thing I would check, should you have a NAT router, would be if the IP address of your local machine is static, and if there is a corresponding port forwarding entry for port 80/8080 (you mentioned trying both) sending all traffic to the corresponding port of your local machine.
Second, I would check
netstat to ensure tomcat is indeed listening on the right local IP address and port on your local machine or 0.0.0.0 (inaddr_any), and not some secondary IP you might have, or localhost (127.0.0.1) only. Relevant options would be:
Which, if everything is fine, would return output containing something like:
TCP [::]:80 [::]:0 LISTENING
I have seen this scenario multiple times (albeit only on Linux, I hardly ever run J2EE stuff on my windows desktop) where tomcat would only bind its socket to the ipv6 address of the machine (ipv6 is usually enabled by default on Windows 7 and most modern Operating Systems), and not ipv4.
When configured to listen on inaddr_any, this resulted in much pain. In this case, simply add:
-Djava.net.preferIPv4Stack=true to the JVM options in the tomcat config files. This could have appeared after a Java update, but is unlikely considering tomcat6 usually runs off a full JDK when properly configured. It is also unlikely since I believe the Linux scenario described above stems from a glibc "bug" (or rather obscure behavior) whose specifics escape me at the moment -- but it is still worth checking, just to make sure.
Should your ISP have indeed filtered port 80 and 8080, I would try some random high port like 6508, just to see if that works better. By all means do update your port forwarding configuration (if applicable) to reflect this.
Unless you provide more details about your setup, I doubt we will be able to assist you any further, sadly :(