I have a 1999 Oldsmobile intrigue, the instrument cluster and fog lamps quit working at the same time. At first it was intermittenent, I would disconnect the battery and reconnect it and it would work again for a brief time. Now they don't work at all. What could it be?

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Yea, take it to a qualified repair shop ! Could be anything , and with out doing some test couldn't make a suggestions .
Headlights/Daytime Running Lights (DRL) Circuit Description
The instrument cluster controls the headlamp systems that include daytime running lamps (DRL). The system allows the headlamps to operate at a reduced intensity when all of the following conditions apply:
• The engine is running.
• The transaxle is not in the PARK position.
• The normal headlamps are not on.
The instrument cluster turns the DRL system on by grounding CKT 592, thereby energizing the DRL relay. This action allows a reduced voltage of 6 volts to flow across the headlamps. If the vehicle has the optional fog lamps, the fog lamp relay will also be energized. The park lamps will turn on and the fog lamps will operate normally. When the headlamp switch is turned to the ON position, the instrument cluster allows normal headlamp operation.
The instrument cluster also has an input from the park brake. If the park brake is in the ON position, the DRL will remain disabled until the park brake is placed in the OFF position. On vehicles with an automatic transaxle, the instrument cluster will disable the DRL until the transaxle has been taken out of the PARK position.

check the plugs behaind the cluster

1999 Oldsmobile Intrigue

IGNITION SWITCH AND LOCK CYLINDER REPLACEMENT

1. Disconnect battery
2. Disable Supplemental Restraint System (Airbags)
3. Remove traction control switch from rear of center console plate
4. Open console lid and remove screws at front of console
5. Pull console plate up to release clips and slide over shifter
6. Pull rearward to release clips retaining instrument panel accessory trim plate to instrument panel
7. Remove screws attaching radio to instrument panel
8. Disconnect electrical connectors and remove radio
9. Take down instrument panel hush panels and disconnect courtesy lights. Remove hush panels
10. Remove knee bolster and knee bolster bracket from driver's side below steering column
11. Remove screws from IPC trim plate
12. Pull out instrument panel cluster trim plate to release from retainers
13. Remove trip odometer and reset switch from IPC trim plate
14. Remove IPC trim plate
15. Remove screws from IPC and pull IPC out
16. Disconnect electrical connectors from IPC and remove IPC from the instrument panel
17. Disconnect ignition switch connectors
18. Turn ignition switch to the ACC position and remove park lock cable from ignition switch
19. Turn ignition switch to ON position
20. Depress and hold locking tab on right side of ignition switch with a small, flat-bladed screwdriver and pull ignition lock cylinder from ignition switch
21. Remove ignition switch bezel from ignition lock cylinder
22. Remove screws attaching ignition switch to bracket
23. Remove ignition switch through the IPC opening
24. To install, reverse procedure

Instrument Cluster -it could be a loose connection at the harness. REMOVAL & INSTALLATION

1. Disconnect the negative battery cable.
2. Disable the SIR system. Refer to procedure outlined in this section.
3. Remove the cluster trim plate, as follows. Fig. 1: View of the cluster trim plate (1), instrument panel (2), dimmer switch lead (3), fog lamp switch (4), and mounting screws (5) - Chevrolet Malibu shown
   Fig. 2: View of the cluster trim plate screws (1), cluster trim plate (2), and instrument panel assembly (3) - Oldsmobile Cutlass shown
   
   1. Remove the bezel from the ignition switch. Fig. 3: Remove the bezel from the ignition switch
      
      
   2. Remove the screws fastening the cluster trim plate.
   3. Gently pry out the trim plate.
   4. Detach the hazard and instrument panel electrical connectors and remove the trim plate.
4. Remove the four screws attaching the instrument cluster to the dash panel.
5. Pull the cluster rearward and detach the electrical connections, then remove the cluster from the vehicle. Fig. 4: Exploded view of the instrument cluster assembly
   To install:
   
6. Attach the cluster electrical connectors and position the cluster into the instrument panel recess.
7. Install the screws into the instrument cluster and dash. Tighten the screws until fully driven, seated, not stripped.
8. Install the cluster trim plate, using the reverse of the removal procedure.
9. Enable the SIR system as outlined in this section.
10. Connect the negative battery cable.

YOU HAVE TO REMOVE FRONT SPLASH SHIELD TO REPLACE FOG LIGHTS.THEN YOU REMOVE THE TWO BOLTS RETAINING THE FOG LAMP TO THE BACK OF THE FRONT BUMPER REINFORCEMENT BEAM AND LOWER THE FOG LAMP.

You need to remove the instrument cluster, then get it out by squeezing the tabs from behind. Here is a pic of the area from when I did my ignition switch:



My website has pix on removing the instrument cluster at http://99intrigue.shutterfly.com/ignitionswitch

You may have a bad instrument cluster. No way to guess sight unseen. Things will need to be tested

Try pulling the fuse for the DRL (daytime running lights.)

Easy - slide under front of car, twist bulb out, twist new one in. Make sure you don't touch the new bulb glass.