Alternator replacement?

Check belt and belt tensioner
To remove the alternator
Disconnect negative battery cable.
Remove right side front drive halfshaft and intermediate shaft.
Remove right side lower splash shield screws and pin-type retainer. Remove 5 bolts and right front lower splash shield.
Rotate accessory drive belt tensioner clockwise.
Remove accessory drive belt from generator pulley.
Disconnect generator harness connector.
Remove upper and lower mounting bolts and generator from vehicle. Remove generator mounting bracket.
Remove generator electrical connectors.
To install, reverse removal procedure.
Tighten fasteners to specification

REMOVAL & INSTALLATION
CAUTION:When battery is disconnected, vehicle computer and memory systems may lose memory data. Driveability problems may exist until computer systems have completed a relearn cycle. See appropriate COMPUTER RELEARN PROCEDURES article in GENERAL INFORMATION before disconnecting battery.

GENERATOR
Removal & Installation (2.0L Zetec)
Disconnect negative battery cable. Remove right front wheel and tire. Remove 5 bolts and right front lower splash shield. Rotate accessory drive belt tensioner clockwise. Remove accessory drive belt from generator pulley. Disconnect generator electrical connectors to voltage regulator. Remove B+ terminal cover, nut and disconnect electrical connector. Remove lower generator bolts.
NOTE:Prior to installing generator, ensure upper bolt is placed in generator.

Loosen upper generator bolt from engine. DO NOT remove upper bolt from generator. Insufficient clearance does not allow bolt to be completely removed. Move generator to rear of vehicle. Remove generator. To install, reverse removal procedure. Tighten fasteners to specification. See TORQUE SPECIFICATIONS.

Removal & Installation (3.0L Duratec)

Disconnect negative battery cable. Remove right side front drive halfshaft and intermediate shaft. See AXLE SHAFTS article in DRIVE AXLES. Remove right side lower splash shield screws and pin-type retainer. Remove 5 bolts and right front lower splash shield. Rotate accessory drive belt tensioner clockwise. Remove accessory drive belt from generator pulley. Disconnect generator harness connector. Remove upper and lower mounting bolts and generator from vehicle. Remove generator mounting bracket. Remove generator electrical connectors. To install, reverse removal procedure. Tighten fasteners to specification. See TORQUE SPECIFICATIONS.

-Removal & Installation (3.0L Duratec)

Disconnect negative battery cable. Remove right side front drive halfshaft and intermediate shaft. See AXLE SHAFTS article in DRIVE AXLES. Remove right side lower splash shield screws and pin-type retainer. Remove 5 bolts and right front lower splash shield. Rotate accessory drive belt tensioner clockwise. Remove accessory drive belt from generator pulley. Disconnect generator harness connector. Remove upper and lower mounting bolts and generator from vehicle. Remove generator mounting bracket. Remove generator electrical connectors. To install, reverse removal procedure. Tighten fasteners to specification. See TORQUE SPECIFICATIONS.

I would try a different alt. Also, there is a fuseable link between the bat and the alt. That sounds like the problem to me but I'm not there to check. Have that checked. NOTE: If the alt is good, the fuseable link will cause this because regardless of the alt's ability to charge to battery, it can't get power to it.