Long (one cycle) incubation with thymidine analogs such as BrdU or EdU, followed by immunofluorescence or click chemistry, respectively, should tell you if your cells / tissues are still replicating DNA or not.
But I'm not sure of what you want to achieve here : just to check if the cell cycle is off, or characterise this arrest (replicative senescence, apoptosis, necrosis, quiescence, ...)?
One small word of caution- many chemical synchronisation methods which arrest the cell cycle at varying points may also affect the cells such that observations of the protein(s) or process(es) are not reflective of undisturbed, steady-state growth.
Happy to discuss further if you contact me directly.