why where they put out of business?

It's because the movie takes place in America, where people will sue you for merely sneezing too close to them. Sadly this was the most accurate part of the film, and really emphasizes what a sorry state this country is in where even if you save the world you'll still loose all your money to the leeches who come out of the woodwork to try to take advantage of the situation for a quick buck. Instead of being praised as heroes the government used the GB as a scapegoat and basically made them villains, which as you can see at the start of this movie, they had become nothing but laughing stocks to the general public. Very sad.

From one perspective, though, their bankruptcy makes sense. There was millions of dollars in property damage and the Ghostbusters were the ones blamed for it since all those ghosts had escaped from their containment unit. It's just like if a lion escaped from a zoo and killed someone, the zoo would be held responsible and heads would roll. I doubt the GB had any kind of insurance to begin with (who would insure a ghost catching business?) and barely had the funds to get the business going in the first place. You can bet the EPA came after them, the city of NYC, basically like Ray said, every government agency who was even tangentially affected by the disaster would try to get some compensation. Not to mention all the lawsuits from regular citizens who had their cars crushed or got hurt during the ordeal. This would add up to tens of millions of dollars that of course the GB couldn't pay, so they had to quit.

But the worst part of all this is that much of the event was surely caught on camera, yet that didn't matter to the courts at all. There were no cameras at the top of the penthouse to see them destroy Gozer, but there were news crews present outside the building when the street erupted, and were surely there when Stay Puft waltzed down the street. Even if you bought Peck's hypothesis that the ghosts were caused by sensory gas, that wouldn't affect the cameras, so there should be no denying the ghosts were real. But because it was all considered fringe science I assume the courts would still refuse to recognize the existence of the ghosts, or at worst, would blame the GB for causing them. Which, kind of in a way the GB did, in that Ray accidentally summoned Stay Puft (but the courts wouldn't know that exactly). I'm sure these trials went on for years, and it's a miracle they weren't sentenced to prison.

Even if the courts did acknowledge the ghosts were real the lawyers would have twisted it in a way to say the GB were still at fault somehow. What I really don't get is why the average person on the street still thought it was fake. Like nobody took the GB seriously, or entertained the notion that ghosts were real by the start of GB2. I mean even the judge in GB2 thought ghosts was fake, so what was HIS explanation for Stay Puft I wonder?