How do you know if a probe is an 'active' one or not?
Price. Active probes cost $100s and you don't end up with them by accident. But really, if it has just a basic BNC connector, then it is passive. Active pobes take additional power. It will come either from the scope (pads near the BNC inputs) or from a separate power supply.
Usually my probes are the typical x10.
That would be a passive probe.
Also, as someone mentioned, the two other pins may be EN and OE, but they could also be a voltage reference for external tuning - assuming this is more than just a 'crystal' opposed to an 'oscillator'.
Do you have those pins connected anywhere on the reference board? From what I see, it is just a typical crystal.
Different oscillators circuits have different sensitivity, I've seen some that handle the probing fine and others that really don't like additional load. You also need to try probing both sides. one of them is a driving output and another one is the input. Probing the output is preferred.
What you need to capture is the startup process. Power cycle the device and capture what happens on both pins in single shot mode. You should see a step from 0 V to some voltage. You may see oscillations on top of that step that die out. If this happens, then CPU tries to enable the oscillator, but it does not sustain oscillation. This may be because of the wrong circuit design or your load.
If you don't see any voltage change, then it does not even try to start and the issue is some place else.