Is this out of the blue, or have you recently done a firmware update? Especially in the latter case, I'm afraid a factory reset is the obvious first thing to try.
To back up your content, copy the files either to a pc or an external sd card - I'm assuming it's mostly photos and music? As long as you have a Google account, your contacts and calendar should be sync'd and will re-load when you set the phone up again. Have a look at your Google account on a pc just to check. If you want to keep SMS and call logs, there are apps on Google Play that can back them up for you.
If you have an external sd card in the device, remove it before resetting as it can be erased in some circumstances. It's also a good idea to make a note, or take screenshots (back them up too), of your homescreens to help with setting them up again afterwards.
If you were to send the phone of for repair, a reset would be part of that process, so you won't have lost anything by trying it yourself.
