Now before anyone says "change the bulb" hear me out...
I had a factory tape player and decided to change it to a factory cd player. I bought one on eBay that the person selling it said that the lcd went out and that sometimes if they would tap the lcd it would come back on. So I thought that I'd just swap the bulbs.
When I received the cd player I took the faceplate off and swapped the whole lcd display out with the one from the tape player (which was previously working). I reinstalled everything and what do you know? the backlight didn't work. I figured I might have installed something wrong. So I tried plugging the tape player back in (with the "broken" bulb) and it worked.
So I opened back up the faceplate on the cd player and tried to see if there was anything out of the ordinary that I could see, which there wasn't.
I know I might be able to jump the power from another power source in the radio to the lcd bulb but does anyone have any ideas what the problem could be?

the pinouts are probably not the same between the two. First, check that the same pin is used for ground. Then check that the same logic board is being used to output to the lcd.

of course, before you do that just look at the LCDs and make sure they are the same model

can you take the bulb out and test it first? make sure you do not have 2 bad bulbs.

I agree with notladstyle that the 2 will probably not interchange.

I used to repair the delco CD players, but 98% of the ones I worked on were the mid 90's style ones out of full size trucks (and similar models with that same radio).

they are set up a bit different from the grand prix style cd players though.

my bulb was bad in mine, so I put 2 LEDs in it, and it works great.