If no change after the standard troubleshooting steps which in order are:
Power your iPhone off and on.
An iPhone reset, which you won't be able to do if the home button no longer works.
Restoring your iPhone with iTunes from your iPhone's backup.
Restoring your iPhone with iTunes as a new iPhone or not from your iPhone's backup.
If no change after the last step, your iPhone has a hardware problem. If you live near an Apple store, you can make an appointment to confirm. Apple won't repair it, but they have an out of warranty or not covered under the warranty "repair" price, which pays for an exchange for the same model at a discounted price off what was the full retail sales price. In the U.S., the cost is $199 plus tax and doesn't require signing a new two year contract with AT&T.