Product review (5 stars): Diagnostics & Installation Instructions for replacing this yourself.
You too can fix the broken ice dispenser lever on your Samsung RF4287HARS!  I did and am happy with the new part.  I just wished it wasn't so expensive.
Run these checks. Does the ice maker still make ice, i.e. you can remove ice from the inside ice bucket and it refills in a few hours? Does the dispenser give you water when you push on the ice paddle?  You have a broken piece of plastic in your dispenser mechanism.  See my first photo showing the bottom, back of a removed ice dispenser.  The plastic arm should be over the black switch on the left.  On the right, you can see the still functioning water dispenser arm.
Once you get the new part, here's how you replace it.  It took me almost 2 hours with cleaning and taking these photos! Hopefully yours will go faster with the instructions below. You will need a phillips screw driver and a metal scrapper.
1. Turn off the water supply to the refrigerator to avoid a mess.
2. The dispenser mechanism is attached to the bottom of the display.  Remove the entire front display, see photos.  The display is held in place by five plastic tabs, two on the right & left, one in the middle on top.  Look closely and you can see them in the photo. One photo shows the right side of the front where the tabs fit into the refrigerator. Avoid scratching the front of your refrigerator by not pry at the front edge. Instead, use a stiff metal scrapper, and slide it up the back of the dispenser area.  Try one side and get it to release and then the other side and finally the top should come loose. The broken plastic arm might fall out as you are doing this.
3. Disconnect the wire bundle holding the panel to the refrigerator.  It's visible in the upper corner of my photo.
4. Remove the other two wire bundles between the panel and the dispenser.
5. Using the screw driver, remove the screw on the bottom of the panel next to the dispenser paddle.
6. Now remove the dispenser.  Others reported that theirs just slid out.  Mine took me 45 minutes to get loose. :^(
If you look at the last two photos, you can see two plastic tabs on the sides of the dispenser that hold it in the two depressions on the bottom of the metal part.  I had to use two scrappers and tap on the metal with a hammer to get mine to slowly separate.
7.  I recommend cleaning the metal and then put a thin layer of oil on the metal.  Be sure to attach the metal back to the panel BEFORE inserting the dispenser onto it.
8. Tuck the wire bundle along the side of the dispenser below the clear plastic tab and then slide the plastic onto the metal part.
9. Clean out the whole dispenser area on the front of the refrigerator.  You won't have this easy of access again.
10. Screw the screw back in.
11. For added safety, you could power down the refrigerator for this step.  I didn't.  Reconnect the brown and black 4-wire bundle to the bottom of the panel.  Reconnect the yellow thru black 5-wire bundle to the top of the panel.  Connect the main wire bundle to the refrigerator.
12. Snap the panel back into place and turn back on the water.
Note, if your display is flashing something like "S" and "E" then the panel needs to be reset.  You can do this by pressing the upper left & right of the display for several seconds where the "Energy Saver" and "Lighting" button are.

If these instructions are helpful, please mark this review as helpful and help others find it at the top of the list!