Check the Rly Ignition 1 fuse (10 A), and the Cluster fuse (20A) fuses in the fuse panel located on the left side of the trunk
Do the radio and AC/Heat control lights still work and can you dim those with the control?
If they are all good, Set a book over the twilight sensor in the defroster duct on the dash. They go bad and will make the dash shut down.
Try pressing the "off" and "warmer" buttons on the heater control panel for five to six seconds, that should initiate a cluster test that will light up all the lights and segments on the dash (except the check engine light).
If none of the above make the dash show signs of life, it is time to repair or replace the cluster. One thing to be aware of, with that cluster you cannot just grab a used one from a salvage yard and plug it in. The cluster is VIN number locked and stores the information for the security key, just plugging a used unit in will tell the computer to not allow the engine to run (thanks GM!), they have to be reprogrammed by a dealer.
There are a lot of companies that rebuild these clusters as they are a common failure item as Ken noted.
Another option is to buy a panel from the same year and split the panel. You basically remove your cluster, take the front display sections off, split the replacement unit. Put the working display parts onto your rear section and put it back together. I have done this twice. Once it worked the other time it didn't, it depends on where the actual failure is.
One nice thing about the repair option is that generally they also replace failure prone parts with better ones.
Here are a couple that I have used with good results, not saying to use them but it can be difficult to find these places if you haven't needed them before.
(these folks are on Ebay as bba-remaninc if you want to see prices)
Friday, January 6th, 2017 AT 2:37 AM