The clutch pedal is going to the floor with no resistance when I press it. I think it is likely that either the master or slave cylinder has gone bad.
You might be right. The slave cylinder is a hydraulic component. When it leaks either internally or externally, it will cause a symptom such as the one you are describing. In your vehicle the transmission need to be removed to gain access to the slave cylinder. This is something I would advise you to seek help from a qualified mechanic for, such as one from YourMechanic. They will be able to help diagnose your clutch pedal issue and make the repairs needed.