Kitchen Electrical Issue, Two Outlets not getting power?

Ok. So There's an issue with two electrical outlets in our kitchen. We got a new kitchen over ten years ago and everything has been kosher up until the last week. I'm no electrician, but I'm able to replace outlets and such and am facing a problem. Originally our 20 AMP 125V GFCI outlet started smoking and stopped working. This outlet is primarily used for a toaster oven along with a switch for the garbage disposal. A couple days later, a regular outlet that is placed in a cupboard solely used for our microwave stopped working. Upon unscrewing the outlet that first stopped working I find that where the hot wire is tapped in from the power wire and to power the garbage disposal is melted. I bought a new 20 AMP 125 V GFCI outlet with a small led light on the bottom right of it. When I rewired everything back up, the outlet still did not work, yet the garbage disposal worked, so power is still going to that. Now heres the weird thing about the relationship with the other outlet. I plugged an iphone charger into it just to see if there was power, and it seemed to get small surges of power but it won't go straight to a charge. As I was doing this, I looked at the other outlet and the small led light would light up. Then when I unplug something from the regular outlet, the led light will go out. Looking to get some solid advice on what to do next. I hit a wall on what to do. Please let me know what you think.

The melted wire sounds like it could be short somewhere. First, if you don't do anything else, go out and get yourself a multimeter. They are fairly cheap and even Walmart often carries them. If they don't then any home improvement store or radio shack will have them. It will allow you to where the power is actually getting to, the voltage etc. It is way better than plugging something into an outlet that may be faulty to see what happens…

Here is one from walmart
http://www.walmart.com/...9/14521541

Start with a receptacle tester or an incandescent light for testing any outlet. Since all of the problems seem to be in the kitchen circuit that includes the garbage disposal, I would disconnect it and then verify that the conductors are secure from the microwave back to the power panel. I'm concerned that the neutral/white wire is compromised in the circuit. Any point where a connection is made should be inspected and all needed repairs are made. If any of the outlets are the quick connect backstab type they should be replaced.
If you still are having problems I will surmise that the problem was caused by the disposal having a ground in the circuit or a severe overload condition and this has caused a cascade of a bad neutral wire and this caused the GFI to fail. None of the problems seem to be that major but several small problems will cause multiple conditions that can be frustrating. Take the disposal out of the circuit and make the needed repairs and then test the circuit before the disposal is reconnected. Good Luck to you. If this does not solve the problem then it is time for a local qualified professional electrician to do the work.

You're describing a very dangerous problem.

First and foremost a wire should NEVER be able to melt because the circuit breaker should trip in the case of any overload situation, whether its a short or an overdraw.

I would immediately manually trip the breaker for this circuit and keep it off until you diagnose and fix the problem.

Start with the above concern. You need to determine why the breaker didn't do its job and protect the wiring. Its most likely a faulty breaker but it could be that someone inadvertently bridged two circuits together. If tripping the breaker stops everything on that circuit from working then it isn't bridged and you should replace the breaker and test-trip it to verify that it's working. The safest way to test trip is to run a microwave, coffee maker, and maybe the disposal at the same time. (you can check wattage and calculate amp draw of the appliances to verify the total is greater than 20A)

Once you know the breaker is working the rest of the problem should present itself. I'm guessing that the disposer will trip the breaker and needs to be replaced. The key is that now you won't burn down your house.