OK it is actually a cct designed for speed control - with a variable voltage output - not really the most appropriate thing to use in this application.
Most monitors (AFAIK) have a 12 volt input - but it would be wise to check that if you can - either from the monitor case or handbook, or a Google search to the mfr's website.
The reasons why you need to check are:
1. The battery has a 12V output - and if the monitor hada 12 v input, there would be no need for this circuit.
2. If the monitor does have an input voltage of less than 12 volts, feeding it with 12V would cause it to draw excess current - which could be why the fuse is blowing.
The other reason for the fuse blowing could be because you have wired it up incorrectly.