Error 678 The remote computer did not respond

If you are getting a 678 error and you can connect using the IP, I would suggest the VPN connection is fine but you have a DNS problem, where the name cannot be resolved.
Are you using a DDNS service with a dynamic IP or do you have an assigned static IP?
If a static IP I recommend using that anyway, but you still need to resolve your DNS issue.
Can you resolve the name by entering at a command line using nslookup, such as:
  nslookup  abc.mydomain.com
You should get a reply like:
Server:  <some DNS server>
Address:  <some IP>
Name:    <yourdomain.ext>
Address:  <your IP>

Yes I am using DDNS and that does seem to be working fine b/c I am running a webserver without any issues.

nslookup returns this:

C:\Documents and Settings\Mike Blanco>nslookup
Default Server:  bgserver1
Address:  192.168.1.2

> bgchemical.com
Server:  bgserver1
Address:  192.168.1.2

Name:    bgchemical.com
Address:  192.168.1.2

Actually it is not working fine. 192.168.1.2 is a private IP and is not routable over the Internet. When you are entering it, it must be from the local network and resolving locally. I think you will find if you try nslookup from another site it will not resolve.

What make and model modem are you using?
I suspect your modem is a combined modem/router and it is using NAT and assigning a DHCP address to your WRT54G. If so you will need to change the modem from NAT mode to Bridged mode. This will allow the WRT54G to appear as if it is sitting directly on the Internet rather than behind the NAT modem. Once you do this the router should automatically get a public IP which will start with something other than;
192.168.x.x, 10.x.x.x, or 172.16-31.x.x
and  then your DDNS, which I am assuming is configured on the Linksys, will also update and repair itself. Let me know what you find and how you make out.
--Rob

I should have been more clear.  I am able to connect to the Public IP address 67.166.x.x via the VPN client machine just fine.  It is the DNS name that is giving me issues.

OK, that verifies the VPN is working but your DNS is not for some reason. When you enter nslookup bgchemical.com it should return:
Server:  <some Internet based DNS server>
Address:  <some IP>
Name:    bgchemical.com
Address:  67.166.x.x
Your results, are from your own server. When I try it from here I get "timed out".

There could be a few reasons for that. One as suggested above a NAT modem, however your VPN would probably not work. Is the WAN address of your Linksys WRT54G  67.166.x.x ? If so that rules that out and the issue would have to be with the DDNS service. Sounds like your VPN is fine as it actually has nothing to do with resolving the name.
Are you using software on a computer or the WRT54G for DDNS?
Which service are you using for DDNS, www.dyndns.com, www.no-ip.com, www.dns2go.com or some other?

Ok I think I am on the same page with you now.

Yes the WAN address on the Linksys Router WRT54G is 67.166.x.x
I am using www.dyndns.com for DDNS and done from the Router.  When I go to the DDNS tab on the Router the Status says that "The hostname does not exist"

DDNS Service :                           
                                      
                      User Name :                      blahblah
                      Password :                       xxxxxxxxx
                      Host Name :                       bgchemical.com
                      Internet IP  Address :        67.166.x.x              
                      Status :        The hostname does not exist

I would bet this is where my problem is but I do not know how to rememdy this.  I have tried turning off DDNS and then renabling it on the router but I still get the same status message.

>>"Yes the WAN address on the Linksys Router WRT54G is 67.166.x.x"
Good.
Is this a static/fixed IP assigned by your service provider, or is it  Dynamic/changing IP?

If it is static, I would recommend using the IP to connect to your VPN. It eliminates 1 more step and increases reliability. However, you will want to resolve for your web server and possibly other services.
Looking at the domain registration information I see bgchemical.com is registered with GoDaddy.com and the DNS servers for DDNS are set up correctly. Sounds like the router is configured properly for DDNS as well, it is pretty straight forward, username, password and domain name. So the problem must be with the dyndns service configuration.

If it is a static IP, I assume you have purchased a "Custom DNS" service. Confirm under the "Cname" section that it shows Host = your domain, and Current IP = your static IP. If an questions about how to configure see:
http://www.dyndns.com/services/dns/custom/howto.html

If it is a dynamic IP I found the FAQ below. You may need to install a software client.

"Why does the DDNS client in my router report "The hostname does not exist"?
Unless the DDNS client in your router has a specific option for Custom DNS, it does not provide direct support for this service. You may be able to make this DDNS client work with Custom DNS by adding "&system=custom" (without the quotes) after your domain in the "Host" field. As an example, instead of having example.com in the Host field you would have example.com&system=custom.
In a few cases, we have seen routers which require that this be enclosed in either single or double quotes. So, if "&system=custom" (without the quotes) does not work, try "example.com&system=custom" (with the quotes) or 'example.com&system=custom' (with single quotes).
If none of these work, you will need to use a software client instead."

You might also be able to register the domain with your ISP for free, instead of dyndns, if it is a static IP.

I am using dynamic dns which Linksys does support on the WRT54G.  I tried the hostname with the "&system=custom" (no quotes) and saved the configuration and got the response "DDNS is updated successfully"

I flushed the dns and registered on my computer and then did an nslookup:

C:\Documents and Settings\administrator>nslookup
Default Server:  bgserver1
Address:  192.168.1.2

> bgchemical.com
Server:  bgserver1
Address:  192.168.1.2

Name:    bgchemical.com
Address:  192.168.1.2

> www.bgchemical.com
Server:  bgserver1
Address:  192.168.1.2

Name:    www.bgchemical.com
Address:  192.168.1.2

You are making big headway, it is working now. From here I get:
C:\nslookup bgchemical.com
Server:  mydomain.local
Address:  192.168.10.212

Name:    bgchemical.com
Address:  67.166.xxx.xx2

Also http://www.bgchemival.com now takes me to your website, assuming it is "BC Chemical handles the Black magic Asphalt..."

The response you are getting is likely due to being resolved internally by your own DNS server which would take precedence over an Internet based DNS server, since it is on the same, local network.

Good deal.  I really really appreciate the help on this RobWill!  I just signed up for this board a few days ago and people have been very helpful including yourself.  I think I plan on staying for a while.

MB

Thanks mblanco2000. Glad yo hear it seems to be OK now. You are right, a lot of great people on this forum.
--Rob