Some authorized dealers handle phone repair. Your owner's manual will also list the manufacturer's address for authorized repairs. Keep in mind, the cost of replacing a phone often is the same as a repair. There are hundreds of companies that make peripherals for wireless devices. The free market system allows innovative companies to provide products and services that some large wireless companies are not as interested in doing.
Batteries have a definite life.
Just because they are rechargeable does not mean they can last forever. Extreme temperature, overcharging and old age can limit the life of your battery. Most wireless phone batteries are rated for 200-400 cycles. That means they can be charged 200-400 times and maintain peak performance. After that, they may only hold a limited charging capability.