I have 4 Viewsonic VA2446 monitors and can only get three of work
The usual troubleshooting of moving ports and cables around will not yield a point of failure.
Any combination will only get three to come on.
The PC is a new Xeon HP workstation.
Will the W5100 actually display 4 independent monitors plugged into the 4 display ports on the back of the card?
You haven't specified how you've connected them. Since those monitors only support VGA and DVI, you must be using at least one active DisplayPort adapter.