When all five frozen food cases are iced up, what is the most likely problem?

When all five frozen food cases are iced up, the most likely problem is a defective defrost timer. The defrost timer is an essential component in refrigeration systems that manages the defrost cycle by allowing the unit to periodically melt away frost and ice that accumulates on the evaporator coils. If the timer is defective, the system may either fail to enter the defrost cycle or have an inadequate defrost cycle, leading to excessive ice buildup and impeding proper airflow and cooling efficiency.

A low refrigerant charge would generally cause decreased cooling and not necessarily excessive icing, as the system wouldn't be cooling efficiently. A defective thermostat could affect temperature control, but it would not directly cause icing unless it malfunctioned in a way that did not allow defrosting to occur. Meanwhile, a plugged condensate drain could lead to water accumulation and not specifically contribute to ice formation on the evaporator coils in the way that a faulty defrost timer would.