How can I retrieve data from an Epic 4G without a working screen?
onik's right that ADB is your best bet for retrieving your apps, data, etc.  But to get it all, you need to be rooted.  XDA has an extremely simple guide for rooting that fortunately doesn't require the use of the screen, it just requires USB Debugging.

Once you root and start adb shell, try entering su before anything else.  If the prompt changes from $ to # then you have root privileges.  If it fails, adb probably gained root privileges automatically.  Now you can access the full contents of the data partition and other areas normally off-limits.