Here is an Old post on your problem

New resistor assembly is about $20 at Advance.

Procedure below:

Document ID# 675187
2003 Chevrolet Malibu
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Blower Motor Resistor Assembly Replacement
Removal Procedure

Remove the right side instrument panel (IP) insulator. Refer to
Closeout/Insulator Panel Replacement - Right in Instrument Panel, Gages, and
Console.
Disconnect the blower motor resistor assembly electrical connector from
resistor assembly.
Remove the blower resistor assembly screws.
Remove the blower motor resistor assembly.

Installation Procedure

Install the blower motor resistor assembly.

Notice
Use the correct fastener in the correct location. Replacement fasteners must
be the correct part number for that application. Fasteners requiring
replacement or fasteners requiring the use of thread locking compound or
sealant are identified in the service procedure. Do not use paints,
lubricants, or corrosion inhibitors on fasteners or fastener joint surfaces
unless specified. These coatings affect fastener torque and joint clamping
force and may damage the fastener. Use the correct tightening sequence and
specifications when installing fasteners in order to avoid damage to parts
and systems.

Install the blower motor resistor assembly screws. Tighten
Tighten the screws to 1 N·m (9 lb in).
Connect the blower motor resistor assembly electrical connector.
Install the right side instrument panel (IP) insulator. Refer to
Closeout/Insulator Panel Replacement - Right in Instrument Panel, Gages, and
Console.