Here are your parts
Replacement parts for FRG FDB4315LFC0 | AppliancePartsPros.com

Here is a tech sheet
http://manuals.frigidaire.com/p.../Kinston/154580201en.pdf

Check your door switches

No, you have to test them.

One way would be to short the wires to each switch together, tape them up so they cannot short to anything else and give it a try.
OR
Use a meter

If doing the short tape a towel or something in front of the unit just in case the pump comes on you do not want to get wet.

Also check that the unit is getting power, you will need a meter for this.

If you do not own a meter, I would suggest you purchase a one. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.