Sorry if you've covered this before:

You said it used to work. Was that with the same computer hooked up to the old satellite system, or just via dialup?

Is your computer's IP address in one the ranges 10.0.0.0 through 10.255.255.255, 192.168.0.0 through 192.168.255.255, or 172.16.0.0 through 172.31.255.255? A simple "yes, it's in one of those ranges" or "no, it's not in those ranges" will do. No reason to tell us your actual IP address if you don't want to.

When you say your VPN client gets to the "signon screen", do you mean it gets to the point where it asks for a username and password?

On the Cisco VPN (I happen to have that one readily available to me), click on your "Connection Entry", then click the "Modify" button. There will be a hostname or IP address in the "Host" field. (This might actually be shown in the main window.) Open a command prompt and see if you can ping that computer.

Let's start with that and see where we end up.