I have a 2002 Buick Rendezvous and the radio and heater control backlights have shut off simultaneously and now only the vent control and trunk release lights work.

I would take a look see at the ground circuits for the none working lights . The incandescent back lighting lamps are then grounded at G200, G301 and G302. You would need factory service info for the location of the grounds .Like this from buick
G200
Right side of the I/P, secured on the underside of the cross car beam, behind the I/P compartment . The I/P compartment is the glove box ,don't know why they just don't say that . You could also check out the power and ground from the componet that's not working ! You can find factory like service info. from alldata
http://www.alldata.com/ . Check out some videos on youtube

https://www.youtube.com/watch?v=efKoWifdcag&t=224s

Interior Lamps Dimming
The second group includes lamps which may be dimmed. This group may use a combination of vacuum fluorescent (VF) illumination and of incandescent lamps.
• The door switches and the window switches
• The HVAC control head assembly
• The radio
• The instrument panel cluster (IPC)
• The steering wheel controls
• The heated seat switch
• The HUD switch
• The lift glass window release switch and traction control switch
When the ignition switch is turned to the ON position, the vacuum fluorescent (VF) displays (radio and HVAC control assembly), incandescent lamps, turn on at maximum brightness. When the park lamps are on and the ambient light sensor indicates low light conditions, all incandescent back lighting turn on at the dimming level indicated by the IP dimmer switch. At the same time all vacuum fluorescent (VF) displays dim to match the indicated dimming level. The BCM L fuse in the console fuse block, supplies battery positive voltage to the BCM. The I/P courtesy lamps supply voltage circuit of the BCM, supplies battery positive voltage to all the dimmable lamps. When the headlamp switch is placed in the PARK position, the BCM will then dim the interior lamps to the dimming level indicated by the IP dimmer switch. When the driver selects a dimming setting by moving, the IP dimming switch potentiometer, all incandescent back lighting lamps are provided with a specific voltage. The incandescent back lighting lamps are then grounded at G200, G301 and G302. When the IP dimmer switch is moved from MIN to MAX, all vacuum fluorescent (VF) displays, as well as all incandescent back lighting respond from Minimum intensity to maximum brightness in response to the IP dimmer switch.
The driver may select parade mode by manually turning on the park lamps during daylight conditions. The front park lamp circuit supplies voltage to the instrument panel cluster, radio and HVAC assembly for a park lamp on input, and the displays will become full bright.