Hi Jennifer. It sounds like your phone can be resurrected but you probably will need guidance from tech support. Borrow a phone and call your carrier's tech support or better yet, in this case, take it into the store so tech support can look at it. A factory reset will erase whatever data you have stored in your phone's memory but should not erase what is stored on your SD card. The levels you have passed in your game apps is not stored on your SD card so you'll have to start those from the beginning again. I hope that is something that can be fixed through a sync in the future. You can find and reinstall all the apps you downloaded or purchased from the Play Store on the 'All (apps)' page, which is to the right (swipe) of the 'My Apps' page in the Play Store. Any apps that sync should reinstate your settings and preferences (like your twitter apps or podcast apps). You will need to reinstall your widgets, wallpapers, and chose your ringtones like you originally did when you got your phone.
This all is a pain but, it can be done. It just takes some patience and a little time. I've gone through it several times. Once you have your phone set up again the way you like it the frustration should melt away.
I found the only data I really, really want to keep is my photos and my documents. I store them on the SD card and back them up to my laptop every 3-4 months. I also use a file manager (like Astrozip or Androzip from the Play Store) to back up my apps. I mostly do that so when an app is updated and then doesn't work well (or doesn't work with my older OS), I can reinstall the older version that I know works well. I never update an app unless I have backed up the working version I am using. As soon as I find out the updated app works well on my phone, I erase the backup of the older version and backup the newer one. Some new versions of apps have expanded permissions that I am uncomfortable with or I'm not interested in the new features that use those expanded permissions. I always can go back to an older version instead of downloading the newer one.
Best of luck!!!