Can I replace my old charger for a new one

Sure, but be sure to follow the advice listed in the "Related Article:"

"If your device still won’t power on or charge, take your device, charging cable, and charging adapter to an Apple Retail Store or Apple Authorized Service Provider for evaluation. You can also contact Apple Support.

* If you aren't sure that an accessory is damaged, take it to an Apple Retail Store or Apple Authorized Service Provider for evaluation, or contact Apple Support."