Two computers on same ISP line - each one start differently

I asked that when cable installed and they advised - no - not necessary. I have checked that also and they both do have different IP - assigned by router according to techs

If you have a router you don't need a second IP address from your ISP. The Router will get one Public IP address from your modem and hand out Private IP address's to your PCs.
If you use a HUB or Switch, all the PC's will try to get a Public IP address's from the Modem. The Public IP address is what the ISP controls and charges you for. They usually only allow you one Public IP address. To use more than one you have to call and ask for additional IP's and they will likely charge you extra for them.
This is assuming the Modem doesn't have a router built into it.

Maybe I am misunderstanding entirely but it appears you are asking why messages show on one and not the other. If in fact that is the question, one pc is set to display the messages and the other is not. VerboseStatus is set by manually editing the registry or through Group Policy.

Code:

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\policies\system

Are all users on this pc admins and are all users accounted for ? Meaning were there any users setup when you first got the pc that are no longer in use.