2004 Chevy Trailblazer water pump

You about to find out that all that junk sold at the discount parts stores with "limited lifetime warranty" is nothing but a marketing ploy to sell total garbage. Go out and get a Delco pump and you won't have the problem. You get what you pay for, regardless of the promises they give you.
The lifetime warranty is worthless if you have to pay labor to change it every 2 years.

Clicking noises? Sounds like an ac compressor engaging, and disengaging. As far as the waterpump goes, they are easy on the trailblazer. If its not leaking, and doesnt move up and down when the serp. Belt if removed, dont worry about it. Your worry should be your compressor. If your ac is on, and that compressor keeps clicking on and off withing a few seconds, then u need an evac and recharge. Have them inject dye because u have a leak. If the clutch is noisy, well then u need a compressor. A garage will charge almost the same to install a compressor, as they will to change the clutch. Thats if they even can. Either way, most times the compressor needs to come out, and the system needs to get evacuated. If it gets opened, dont be surprised if u need a reciever dryer, its not a ripoff.