I will try to help you. Disclaimer: I'm not a repair person and I'm not a specialist. This is what I do and you act at our own risk.
Take the cartridge out. You will lose at least one photo. If you want to prevent this, consult the web how to avoid.
Check the voltage of your cartridge. It should be more than 6 volt. If not, your cartridge won't work and you will have to get a fresh one. That may solve your problem.
If the voltage is fine, you can try to reset your camera. This is how to proceed:
On the left side of the SX when you hold the lens towards you there is a black plastic piece that covers a series of gears. To remove it, you just have to lift this piece, starting at the yellow lever where there is the white arrow on a black background. It is just clipped in, no need to force it.
Then you have to turn one of the dented wheels that act as a gear. It's the second but last towards the back, it has to be moved counter-clock-wise. Look at the photos of a French website here
https://www.polaroid-passion.com/forum/viewtopic.php?f=5&t=2375 to locate the gearwheel.
On a full cycle, you will hear a mirror up sound, sight of the viewfinder is obscured. A long time after having continued to turn, you will hear a click of the bottom lock of the mirror, one can see through he finder again. End of the cycle. Going through the cycle again doesn't harm the camera, but it may help an old camera to come to life again.
Good luck!