Hi, I think the first thing you should do is going to try "wake up" your phone first. Repair shop can help you a lot. But you also can do it by yourself, but you need to make sure you have the ability to control everything in the operation you try to turn on your phone. You can search many method on Google about the refurbishment. If you have no idea about how to perform you'd better go to the repair shop.
But one thing you need to pay attention to is that after refurbishment (which means you got a new system on your phone like Android 4.1.2 or higher), all the data on your phone will be gone. This is because the refurbishment operation will give you a "new" phone-I mean the system. So the data will be gone. But actually you still can get them back by some tools or apps which allow you to sync your phone with your computer and run the recovery tools/apps on your computer to recover your data on your phone.
Here I suggest you after you get back your phone, don't put any new files into your phone 'cause if you do this, the data overwritten will be caused and you will lose the chance to recover your data.
The data recovery operation is not so complicated, you can visit this post to get more details and see if it can help you or not,