There might be a hardware problem but as well it could be just software related. Try reinstalling the device firmware.
Install Nokia PC Suite for your phone and the drivers if you haven't already done that!
First of all, you'll need a program and the necessary firmware files:
1. Phoenix Service Suite (2012 or any other version. Search for it on Google)
2. Nokia 7310c firmware (RM 379 DP20 3 00 sw 09 40 7310c
Install Phoenix Service Suite, extract the software (it will auto-extract the necessary files in the right folder, but first it is necessary to install Phoenix).
Now, after staring Phoenix, do the following:
1. Click File > Open product (not Open profile!)
2. Select RM-379 from the list (you can type that in the "Type filter" text box to find it faster)
3. Select the product code (RM-379) from the list and press OK
4. Now press Flashing (at the top menu, where is also File)
5. Check Dead phone USB flashing on the new dialog box that appears.
6. Click the browse button at the Product code input (top section of the new dialog box)
7. Select an option. Any will do. The difference is between regions and languages. But since I don't know from where are you or what language you'll need on your phone, I can't tell you exactly what to choose. But all region files have "English" avaible
8. Press Refurbish. Take out the phone battery, insert the USB cable, then insert the battery. If any dialog pops up, press OK.
8* At this point, DO NOT DISCONNECT THE USB CABLE until the process is finished!
This process should take about 5-10 minutes and after it is finished, the phone should boot up by itself and everything will be fine.