You state - no codes displayed.
Do you mean on the vehicle dashboard, or do you mean when you plug in a diagnostic code reader?
I am aware that these vehicles suffered with Catalyst efficiency failures, and also the intake manifold gaskets would degrade as they were made of rubber.
When they degrade - they allow excess air to enter the intake which affects the fuel air mixture process of the combustion burn.
Also - there is a vehicle crank case / emissions pipe which goes from the Camshaft cover to the throttle body / intake manifold - these used to degrade also. From above they would look ok - but underneath they had collapsed in on themselves and turned back to a tar like substance.
I hope this helps you resolve your concern.
I don't understand how the vehicle can be in limp home mode without the engine mil fault light being illuminated.
As your have checked all the obvious physical possible concerns - the next step would have to be a fault code read and then extended diagnostics using equipment to read the live readings of the oxygen sensors, the mass air flow meter etc.
The fault codes that are logged - may well give you the obvious answer straight away.
As it stands now - I think you have done all your preliminary diagnostics - now it is time to plug to the vehicle.