[robespierre]

Degaussing is for fixing color purity problems, which this isn't. This is also a Trinitron monitor; strong degauss coils can damage them and it is very rarely needed.
What is needed here is a source of test patterns. You can only diagnose what appears on a display if you have full control over the input signal.
One possible reason that the display appears magenta all over is that the opposite of magenta—green—is missing. Using a test pattern that is all-red, all-green, and all-blue, in order, will show if any color is missing.
Then if it turns out green is missing, there are several possible places where the missing signal may be coming from. A broken input connector pin or a broken cable would do it, as would a fault in the green channel video amplifier, or a problem with the green channel cathode in the CRT tube itself. All electronic repair relies on differential diagnosis.

Some ideas for diagnosis of this type of problem are here