My iPhone 4 doesn't show the sign of a charging battery and takes hours now to charge

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/