I am assuming this is a CO2 laser tube for use with a high voltage, like a lot of low to mid range lasers use.
The best test is just trying to fire it and checking for indications of what's going on. If you have a camera that can detect IR, then you can use it to look for a purple glow when the laser is firing. A lot of smart phones can pick up IR light. You can test your camera with an IR remote control and look for some purple light.
If you see a purple glow on your tube when you fire the laser then the tube is not dead, so check mirror alignment, lens, etc. If there's no glow, then it's not firing, but it could be the power supply or controller rather than the laser tube. If you noticed a decrease in power over time before it failed, that's a good indication of tube failure. If it happened suddenly, you should suspect other components, most likely the high voltage power supply.
You can check the power supply with a large resistor designed to test high voltage systems and a multimeter, but the voltage on the high power side will be in the 20kV and above range, so make sure you have the proper knowledge and equipment to test it safely. If you can't tell, I'd recommend replacing the power supply before buying the tube since it's usually cheaper to purchase and ship the power supply, and if you find out that it's not the problem you can return it more easily and then buy the tube.