Checking the condenser is pretty easy. I would do that for sure to try and rule it out. Disconnect it for this test.
Take an old school type VOM (volt-ohm-meter), one with an actual needle type meter movement (because they work best for this) and set it in the ohms position at R-x100 or x1000. Connect the leads one direction and you should see the meter needle "pulse" and then decrease to infinity as it charges. Then remove the leads and set meter to 10 volt DC and touch again. You should see the needle deflect and then go to zero. If you do not get these results, try reversing the leads on both tests.
These are pretty simple capacitors that are non-electrolytic, meaning that they are, I believe, like an A/C capacitor and not polarized and usually of a dry type.
If from a quality manufacturer, they are pretty robust and last a very long time.
This is not a definitive test, but will see if it is shorted or has too high of a resistance level.
If you have a more advanced meter, they often have a capacitance testing function.
I myself have a dedicated capacitance testing meter that I use for motor, power supply and electronic caps, but they can be pricey. They however will give you the value in micro-farads of the cap which can be compared to the manufacturers value.