The dimmer light lead on the car's radio harness (not the actual harness that's on the radio) is either shorted or grounded. I've had this issue before on my Cutlass, no fuse blown but it would act weird sometimes. Basically the "orange" wire is touching the metal chassis of the aftermarket head unit or you wired it wrong when you hacked off the stock clip. Regardless, your issue may lie around there. On the Alero side, it should be a gray wire that's placed bad.
Here's also the color codes for the Alero's radio harness, if you want to verify that you put back the clip on right.
Graham may have posted the same info that I did in his pics, but I find those diagrams hard to read. I probably should learn how to read those schematics but anyways...
TLDR, check your dimmer wire on both the radio and Alero harness.