2004
Fixing the timing belt does not always guarantee the car will run. In some cars, it can mess up the valves.
A quick search tells me that this car has a known timing belt idler issue (poor quality plastic idler pulley) that can fail ... as a 2004 model your car is over 10 years old and all manufacturers recommend replacing a timing belt before 10 years no matter the mileage...
The timing belt failure could have damaged the head and pistons... I would pull the cover off of the belt and if the idler is damaged/worn/loose I’d try to get GM to fix it.. it seems they are doing that under a hidden warranty ,, of course the age, mileage and whether you bought the car new or used will come into play..
I consider it to be a good car to zip around in for chores ,, worth fixing if it’s not too much $$$.