It's not unusual to have some problems with your iPhone software because there is so much technology in so little space and you can't expect it to work flawless all the time. After all machines are just machines and they do break from time to time. That is why you need a consult from experts who know what to do in this situation or a very fortunate answer from another iPhone user who experienced the same problem some time ago.
I did some search on these forums and found out more possible answers to your problem. The explanation for the fact that your iPhone stays stuck on Apple screen is that something went wrong during your downloading or installing a software application and it did not install completely, but also blocked the entire iPhone and its operating system.

You can solve the problem yourself, even if you are not so much into technical problems. The first thing you have to do is reset your iPhone, so you can do this by simply holding the sleep/wake button and the home button at the same time until it turns off. Release them when the iPhone is turned off because if you keep pressing the two buttons your your iPhone will turn back on.

Next you will have to try to connect your iPhone to the iTunes and leave its recovery to this software. In order to do this you will have to connect the iPhone dock to your computer and start running the iTunes. Then it's time to take the iPhone again and hold the home button while placing it on its dock. Keep pressing that button after placing the iPhone on the dock and hopefully you will be able to see the following message on the display : Connecting to iTunes. The problem is almost solved if the iTunes recognizes your iPhone.
If it does, you will be asked if you want the iTunes to perform the recovery for you. Select RESTORE and then choose to restore from the backup. It should fix your problem and your device will be running again. You will be able to perform all actions and the only thing you will lose is your music. But don't worry, you can get some more music on it in no time.
If you want to see a video tutorial with all the steps you need to take when doing this just follow this link to YouTube.