"There is already a default route using the 0.0.0.0 for internet address and netmask, with the next hop being set to the ip of our firewall in another site? Is that correct?"
How does your remote site connect to the firewall at the other site? Is it a leased circuit directly to the other site or does it go through the internet via dialup/dsl/cable modem/frame relay/atm/etc provided by an ISP?
If it is a leased connection then the next hop being the firewall is probably correct if the firewall and the HP router are on the same subnet.
If it is via the internet then No. The next hop has to be on the same subnet as the WAN interface of your HP router. Normally this IP address is provided by your ISP (either manually via email or letter at initial turn up or it is provided automatically by DHCP each time you connect and is then subject to change) and is actually the IP address used on their router on the interface which connects to you.
Assuming a leased circuit (which seems likely since you do have connectivity for email etc) there are several possible problems which could prevent connecting to the internet.
1. Your remote site uses non registered addresses and the firewall is not doing NAT for you. Your packets may actually reach the internet but they are probably being blocked by the ISP's router and if by some chance they make it to a host then the internet host has no way to get back to you since private addresses do not appear in the routing tables.
2. The firewall does not have a rule allowing your traffic to go to the internet (and return).
3. The firewall does not do routing or does not have a route to the subnets on the Ethernet side of your remote router. A lot depends on how you connect to the firewall and whether the firewall considers the remote site to be on an Inside or Outside interface.
4. The HP router (or some other router in the path) may be filtering port 80 or only allowing connection to company LANs and dropping the packets.
5. There may be no DNS administered on your Hosts or they may not be able to see it do to routing or filtering or authenication problems. On a host on the remote side do:
nslookup hp.com
and see if you get a reply back like:
C:\>nslookup hp.com
Server: d903chz10039.directvla.com
Address: 172.16.1.2
Non-authoritative answer:
Name: hp.com
Addresses: 192.6.234.9, 192.6.234.10, 192.151.52.187, 192.151.53.86
161.114.22.105, 192.6.234.8
If it doesn't connect to the DNS then that's part of the problem.
You can try a trace to hp.com from a remote host and see if it at least gets past your firewall (though many firewalls will block trace especially if they think you are on an outside interface)
Unix/Linux
traceroute hp.com
Windows
tracert hp.com
The trace will not complete because HP's firewall stops it but on my system it gets 10 hops and stops at 63.146.178.244.
If you want to send me more detailed info about your architecture and the results of the nslookup and trace via email I can probably tell you more.
rkinner(at)att(dot)net
Ron