Can I do anything besides buying a new phone?

Hi, follow the steps on here to change the battery, except dont remove the battery, and clean the terminals with isopropyl alcohol and gently try to remove the corrosion. There are a lot of videos on youtube also to help you. Watch a couple of them and try it. Write back on what u did. Good luck.

Mario, you did not tell us which pins are supposed to be corroded. If it is the dock connector, replace it by following this guide. Since you will have to open your phone, you might as well clean it. Use this this guide for that task. It was written for the 3G but all the points apply to your phone as well. Replace your battery as well and reevaluate. See what damage, if any, you really have. Also, make sure you try a different cable. Check these answers as well as the ones on here. I don't think a new phone is the way to go, at least not yet ;-) Hope this helps, good luck.