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Replacement parts for FRG FRS26R2AWA | AppliancePartsPros.com

I have been looking at the coils but cannot see leak!
Leaks can be difficult to find. Sometimes you will see what looks like a wet spot (oil) at the leak location.

Also does the capacitor have something to do with the frig not getting cold?
Yes, if the compressor does not start.

The cost of these repairs was too high. The frig is in good condition.
Often if you have a leak or a compressor failure, it makes more sense to replace the unit due to the repair cost. Also it makes little sense to recharge a unit unless you can find the leak.

Does it really need a new coil? The frig is only 6 years old.
Cannot say without actually being there. Also do not know what coil they are talking about, you have 2, evaporator and condenser

First is the compressor running.
If not the low/no freon is probably not your problem.

If it is running remove the evaporator cover in the freezer section and check out the evaporator coil. If it is cooling only where the freon enters the coil (often you will see frost in this area) you are probably low on freon.
If there is no cooling then you are probably out of freon.
Either one is bad news.

Here are a couple good sites with basic repair help which should be useful in troubleshooting this problem.
http://www.applianceaid.com/frig.html
Refrigerator Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com