Just replacing parts isn't the way to fix this problem , viewing wiring diagrams too see what all is involved in making the wipers work is . Then using a digital volt ohmmeter to test electrical circuits . Also looking at factory service info. to see how it's suppose to work.
Free wiring diagrams here http://www.bbbind.com/free-tsb/
Enter vehicle info. year , make , model an engine size . Under system click on body & accessories , then under subsystem click on wiper/washer . Click the search button ,then click the blue link. Looking at the wiring diagram i see two fuse's an two relays that are controlled by the BCM - body control module . Also hooking up a scan tool that can read BCM DTC'S - diagnostic trouble codes could be helpful . The wiper switch is a input to the BCM - the BCM will energize the relays to turn on the wipers.
Wiper/Washer System Components
The Wiper/Washer System consists of the following components:
• Windshield wiper/washer switch
• Body control module (BCM)
• Wiper 1 relay
• Wiper 2 relay
• Wiper diode
• Windshield wiper motor
• Windshield washer pump
• Windshield washer nozzles
• Windshield washer solvent container
• Windshield wiper arm and blade assemblies
• Windshield wiper transmission
• WIPER/SW 10A fuse
• WIPER 25A fuse
Wiper/Washer System Description
The body control module (BCM) controls wiper motor low speed operation. The washer pump and high speed operation are controlled directly by the wiper/washer switch. The windshield wiper/washer switch supplies voltage on the signal circuits to the BCM for windshield wiper/washer operation. When WASH, MIST, DELAY, LOW, or HIGH is detected, the BCM energizes the wiper 1 relay by suppling voltage to the relay coil. This allows battery voltage from the WIPER fuse to flow through the relay switched input then through the contacts and out the relay contacts to the wiper 2 relay switch contacts. Since the wiper 2 relay switch contacts are normally closed to the low speed circuit of the windshield wiper motor, the motor will operate at low speed.
DTC B3715 02: Front Wiper Relay Drive Circuit Short to Ground
DTC B3715 05: Front Wiper Relay Drive Circuit Short to Battery or Open