Probably chemicals in film pack is already dried out. I assume it's an old Polaroid camera ( You haven't posted the model which is something important) so only way to test the camera is buying a new film pack from Impossible Project. That's only if you camera is either Polaroid 600, SX-70 or Spectra models. It's really not worth spending money on these old relics unless you are a vintage camera collector. Most of these won't work anymore and film packs are really expensive. Like 25 usd for 8 photo prints. These days there are so many new cheap instant camera models out there. Just check these and buy one because these new cameras work better and produce better quality photos and also film packs are lot cheaper.

Yes you can use either Zink PoGo paper or Zink Premium photo paper. Only difference is Premium paper doesn't have a white border so image will be printed on whole paper. Also they say colors are improved but I don't know if it's true or not.

You need to push it back very carefully making sure 2 parts connecting correctly.

Remove the film pack and use a new one. There is a good chance somethings wrong with that film pack you have in camera.

Since the Film pack was inside camera all these years I don't think it's in working condition (Film pack). Buy one of those Impossible Project 600 film packs are test the camera. Those new packs cost you around $24. From what you said I think camera is still working. But the problem is are you willing to spend $24 for 8 photo prints ?

Did you use one of those old expired Polaroid 600 film pack or a new Impossible Project film pack ? There is a good chance something wrong with the film pack than camera. My guess is half dead battery specailly if you used an old Polaroid pack. There is a little chance you have a dead battery problem with Impossible Project packs but you can never be sure. I guess only option you have is trying another pack.

You don't need to install batteries for Polaroid 600 series cameras. These cameras use Integral film packs which has an inbuilt battery inside the pack. basically camera is powered by the film pack. This is why you shouldn't buy old expired Polaroid film packs. There is a good chance you end up with a pack which has dead battery. Only use Impossible Project 600 packs which are in production. So you shouldn't have a Polaroid 600 battery problem. These Impossible Project film has very powerful battery they even ask you to return those once you used the pack.

Sadly I dont think you can get it fixed if it was fallen while you had camera On. Something probably short circuited and fried. See if your local camera store has repair guy who would willing to give it try.

Did you try a different film pack ? I was told few people found this red blinking light problem was gone when they change the film pack. Yeah might loose a good pack but you need your camera to work so...

Did you check shopping malls and Camera stores ? Check online and call local camera stores. One another way is buying from ebay.