I just finished reading this about the FORD PCM controlled alternator...
Look at the second page...they made comments about replacing multiple O'reilly alternators (which I think you were trying to say " from Oriel's store")...
Part 1 -Ford P0620 Test -Alternator Diagnostic Test
You may have another bad BATCH of re-manufactored alternators...
O'Reillys, Advance and AutoZone both have lousy "remanufactored in MEXICO" alternators and starters ...Most of them DO NOT WORK... That's why they have a "Lifetime Warranty"..
You take them back UNTIL you get a good one...
The Mexican remanufactored alternators are only "repaired" and not truely remanufactored...
A TRUE remanufactored alternator will have
New Bearings...
New Bridge rectifier
New Regulator (in your case a partial regulator)
New Brushes
New insulating washers...
Then they are tested and burned in...
These Mexican rebuilts are repaired sometimes "if" they find an actual problem with it..
If they don't (if it's intermittent) they clean it up, paint it and ship it out... If you are the unlucky guy that gets one of these you spend hours replacing yours with another BAD one... The car parts dealer will "Happily" exchange the bad one with another that may be just as bad as they have very little money involved in the one they sold you...
AND this bad one will go through the same "quality control and repair" once again and some other unlucky guy will get the same problem...
Because they don't replace common failure parts like in a true remanufactored alternator this problem happens...
You might want to buy a NEW alternator or have yours rebuilt by a quality starter/alternator rebuilder...
Funny...my 06 and 07 KIA Spectras have alternators with the regulators built in... They are cheaper and not as "advanced" as your 04.
Dave