Hi Dorothy, I've got the same problem a time ago. Maybe you settings for dpi were too high or the dimensions for the scan too big. Than the memory become full and the whole thing stops.
Uninstall the Epson (-> Software -> Uninstall) and shut down your PC.
Wait for several minutes so the memory can be empty, disconnect the cables.
Restart your PC and install the software again. Connect your cables and reboot.
Normally that must clear the problem.
If you did all this and the problem consists there is something worse with the hardware.
Greez,
erjie