Hi,
The purple wire will be on the starter itself. If it has power when the key is in the start position, the battery is charged, and the connections are all good, it sounds like you have a bad starter. If you look below at pic 1, I highlighted the purple wire on the starter.
At this point, disconnect the battery and remove the starter. Have it bench tested at a local parts store. Most do it free of charge.
Here are the directions for the replacement of the starter motor.
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1998 Oldsmobile Aurora V8-4.0L VIN C
Starter Motor Replacement
Vehicle Starting and Charging Starting System Starter Motor Service and Repair Procedures Repair Instructions Starter Motor Replacement
STARTER MOTOR REPLACEMENT
REMOVAL PROCEDURE
Caution: Refer to Battery Disconnect Caution in Cautions and Notices.
Pic 2
1. Disconnect the negative battery cable.
2. Raise the vehicle with a suitable safety stand.
3. Remove the splash shield.
4. Remove the flywheel inspection cover bolts.
5. Remove the cover.
6. Disconnect the starter motor wiring.
Pic 3
7. Remove the starter motor mounting bolts.
8. Remove the starter motor.
INSTALLATION PROCEDURE
NOTE: Before installing the starter motor to the engine, secure the electrical terminals by tightening the nuts next to the cap on the solenoid battery terminal and on the SD-255 S terminal. If these terminals are not tight in the solenoid cap, the cap may be damaged during installation of the electrical connections and cause the starter to fail later.
Pic 4
1. Install the starter motor.
2. Install the starter motor mounting bolts.
Tighten
Tighten the bolts to 43 N.M (32 lb ft).
NOTE: Refer to Fastener Notice in Cautions and Notices.
3. Install the flywheel inspection cover.
4. Install the cover bolts.
Tighten
Tighten the bolts to 7 N.M (22 lb in).
Pic 5
5. Connect the starter motor BAT terminal wire.
Tighten
Tighten the BAT terminal nut to 16 N.M (12 lb ft).
6. Connect the starter motor S terminal wire.
Tighten
Tighten the S terminal nut to 2.5 N.M (22 lb in).
7. Lower the vehicle.
8. Connect the negative battery cable.
Tighten
Tighten the cable bolt to 15 N.M (11 lb ft).
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Let me know if this helps or if you have other questions.
Joe
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Saturday, November 21st, 2020 AT 8:54 PM