I owned a PRO-2006 many years ago. Very good radio for aircraft monitoring.
The service manual is available online.
http://www.radiomanual.info/schemi/RX/Realistic_PRO-2006_serv_4.0.pdf
Looking at the block diagram I was reminded this is a triple conversion receiver. The AM and NFM (not WFM for FM broadcast) are detected after the same IF Mixer. So if receiving FM (called NFM in the block diagram) signals is not distorted then we know that things are ok out of the 3rd IF mixer. So then the problem is likely in the "AM IF AMP/Detector" circuit (Q12,13,D33), the AM AF Preamp (Q18,D34) or maybe the Switching circuit for NFM/AM that selects the detected AF to be routed to the audio output.
I think that switching circuit can be ruled out if you tune to a constant signal such as ATIS or AWOS/ASOS and see how it sounds in AM vs FM mode. If it sounds the same, maybe AM mode isn't actually being selected and the switching circuit is at fault. That circuit is controlled by the CPU, but I doubt it is the CPU, it may be any connection to the CPU. If the AM vs FM mode does not sound the same, then we are probably looking at an issue back at Q12, Q13 or Q18.
There are some electrolytic capacitors in those circuits, so as suggested by other posts, I would certainly try changing them first. Much less likely to be a transistor or other discrete component. I suppose it may be an AM detector diode, but I would go for the capacitors first and then the diodes. Checking the parts list, D33 and D34 are germanium diodes (type used as AM detectors) and they both are in the AM detector circuit.
One other thought looking at the block diagram and observing how the Zeromatic circuit gets input, I wonder if it may be improperly correcting the signal tuning. I would need to study that circuit more, but sort of looks like it could affect AM mode differently than FM mode. If you are using Zeromatic, try turning it off. If that is the culprit, just don't use it.
