The "weak" button is a good idea (to allow focusing) but a very poor implementation which self destructs.
If the fan is working you know the laser module is getting power, which means the diode or more likely the driver circuit is dead - either way, the seller should offer some "fix". I would ask for a discount on the TTL laser module.
The L7 is cheaper but a good laser with TTL driver is the best solution for multiple reasons.
I recommend the 2000mW TTL laser that Banggood sells, but now they have several more options which I haven't tried.