Age maybe a factor - but my AC is from 92 and it works fine albeit doesn't get used often and I clean/maintain it annually.
If your sure your getting ample shore power then take off the shroud and inspect the unit .. clean both the condenser and evaporator coils (use forum search feature for how to clean evaporator coils) .. while your up there inspect the start and run capacitors sometimes a bad one can be identified because of smell or deformation - they don't cost much to replace. Check the fan motor .. older units may have fan motor that requires periodic lubrication (mine has oil hole). Also - clean the air intake filters located inside the rig.
Those are the free/inexpensive things to check out. Compressor issues are big ticket and would usually require replacement of unit.