2005 Ford Freestyle engine and lights problem
 

I have a 2005 Freestyle with 218k miles.
A couple of months ago I bought a re-built alternator thinking that I should replace the alternator due to the mileage and not wait until it breaks.
Shortly after the installation, the lights on the dash, radio, headlights started dimming for a split second and they would come back to normal brightness. It would do this all the time.
I read online that this happens when installing a rebuilt alternator.
I was willing to live with it, but last week the car started to run rough at times as if it had a bad ignition coil.
I figured the alternator was the culprit and bought a new unit and installed it.
Now the car still runs rough however, once it starts, the lights on the dashboard and all gauges go dead.
If I set the key to ignition without starting the engine, the gauges on the dash work. As soon as the car starts, the dashboard gauges go dead, the running rough returns.

I contacted an electronics/automotive repair shop and inquired. I was told that the symptoms my car has, are not related to the PCM (Power control module?).

I connected a scanner and there are no codes in the system.
Where should I look next?
I would appreciate any advice anyone can provide.
I have looked in youtube, there are other Freestyles with similar problems, but no one posted a solution.
Thank you
RG

There are some things we just need to know.
Where did you purchase the alternators?
What does "new" mean?
Ford alternators are a funny bunch and for some reason rebuilders just can't seem to get them right.
Awaiting your replies.

Hello there.
The first alternator I purchased was a remanufactured unit made by Bosch and sold through Advance Auto.
The second alternator I purchased was a new alternator from Rock Auto, made by Remy. The alternator was advertised as a new unit and the box it came in had a label "new".
Thank you for any advice you can provide.
RG