Instrument lights go out and a click at the fusebox would lead me to belive that it is either a relay or a starter issue.
Performing the starter relay test.
(3) Perform a visual inspection of the starter/starter solenoid for corrosion, loose connections or faulty wiring.
(4) Locate and remove the starter relay from the Power Distribution Center (PDC). Refer to the PDC label for relay identification and location.
(5) Connect a remote starter switch or a jumper wire between the remote battery positive post and terminal 87 of the starter relay connector.
(a) If engine cranks, starter/starter solenoid is good. Go to the Starter Relay Test.
(b) If engine does not crank or solenoid chatters, check wiring and connectors from starter relay to starter solenoid and from the battery positive terminal to starter post for loose or corroded connections.
Particularly at starter terminals.
(c) Repeat test. If engine still fails to crank properly, trouble is within starter or starter mounted solenoid, and replace starter. Inspect the ring gear teeth.
WARNING: CHECK TO ENSURE THAT THE TRANSMISSION IS IN THE PARK/NEUTRAL POSITION WITH THE PARKING BRAKE APPLIED. THIS MAY RESULT IN PERSONAL INJURY OR DEATH.
The starter relay is located in the Power Distribution Center (PDC) in the engine compartment. Refer to the PDC label for relay identification and location.
Remove the starter relay from the PDC as described in this group to perform the following tests:
(1) A relay in the de-energized position should have continuity between terminals 87A and 30, and no continuity between terminals 87 and 30. If OK, go to Step 2. If not OK, replace the faulty relay.
(2) Resistance between terminals 85 and 86 (electromagnet)
should be 75 ±5 ohms. If OK, go to Step
3. If not OK, replace the faulty relay.
(3) Connect a battery B+ lead to terminals 85 and a ground lead to terminal 86 to energize the relay. The relay should click. Also test for continuity between terminals 30 and 87, and no continuity between terminals 87A and 30. If OK, refer to Relay Circuit Test procedure. If not OK, replace the faulty relay"
Hope this gets you started. You can download the service manual from here Good Luck.