If you can't get your controller or software to fire the laser, you can make a simple harness to test just the power supply and tube.
Warning! This is of course potentially very dangerous. Be very careful when doing this. The electrodes must be properly connected to the tube. Stay away from all tube electrodes. Make sure the tube has a suitable target to fire at like a fire brick. Wear your safety glass. Make sure the tube cooling is running.
Make a simple test harness like the one shown below.
You can either hook the test button from H to 5V or L to ground
Most laser power supplies I know about are specific to the line voltage, so you must be sure to get a 110V or 220V version. The power input is usually a terminal block labeled FG, AC and AC. FG is ground and the AC terminals are wired with hot and neutral (US Terms). Hot and neutral can go on either AC termnial.