Possibly but there's some troubleshooting to try.
Is the iPhone 4 running iOS 6.1.3?
What is the wifi network name? If it's a common name, this can cause problems: http://support.apple.com/kb/HT4450
Does it work on other wifi networks or is it just this one?
General wifi troubleshooting: http://support.apple.com/kb/TS1398