I have 3 ESQ 1 cartridges here that are unfortunately no longer active. I.e. I can no longer control the patches in the cartridges, there is, so to speak, nothing more. Are these doomed or how can I actively use those cartridges again? It is not the cartridge port in the ESQ1.

The ESQ-1 cartridges have batteries in them which will eventually go flat. Try replacing the battery and see if that is the problem.