Could be the charger/cord, could be the phone.
Basics from the manual are restart, reset, restore
Follow the 3R's- if a restart does not solve your problem proceed
User troubleshooting is:
1.restart, ie power off/on,
2. reset http://support.apple.com/kb/HT1430,
3. restore from backup, restore as new device. http://support.apple.com/kb/HT1414
You can always make Genius reservation http://www.apple.com/retail/geniusbar/