Fridgedaire frs23lh5db1 ice maker not working

fridgedaire frs23lh5db1 ice maker not working. this fridge is used and when i got it the green plastic line at the back of the fridge was cut and missing a 2' section of line. i spliced the line back together, hooked up the water ( i get water out the door now) plugged it in and flipped the ice maker bar to 'on'. after a few minutes i heard a noise that sounded like the 'pump' had kicked in and i noticed that the line to the ice maker at the back of the fridge had filled up with water. I waited patiently for 4 or 5 hours and when i went to check for ice there was none. I removed the ice tray and stuck my fingers in the ice maker tray and it was dry. i felt underneath the coils of the ice maker and burned my finger! I guess it has a coil to heat up so that the ice falls out and the cycle can start over. is the heat a malfunction or did the tray just fail to fill up with water? is something missing from the back of my fridge that ought to be there?