2003 Mazda 6 v6

I started my car a few weeks ago and it ran really bad and almost didn't have power to get out of the driveway. By the time I got turned around and back home, about a block later, the car had died a couple times and I noticed the front precat was glowing orange. The next day the car started fine and drove for a while with no problems before the engine light came on (maybe 50 miles later) and I took it and had it checked. The shop said it was code P4031 and that all my cats needed replaced. They quoted 4k. The car ran fine the 4-5 times I drove it after the shop diagnosed it with what felt like minor power loss. I bought the cats online and the day they showed up I had to make a run in the car and it just wouldn't run at all. It starts but dies after maybe 1 second.

I just recently bought this car so really don't know it's history. It only has 81k miles on it. I read bad cats can cause the engine to blow. Do you think my engine is blown? Is it worth towing to a shop to see if replacing the cats will make the car run? If i cut the cats off with a saw-zaw or drill some holes in the exhaust would that allow my car to run if it is the cats for a test?