This is a job I believe you can do yourself. You have done an excellent job so far.
Go to www.partselect.com this is a site where you can order your parts you need.
Here are the part numbers for that web site.
Defrost heater PS303265
Defrost thermostat PS 303545
Both of these parts are where the coils are where all the frost is. Just to double check what you have done. When the fans stopped, when you were turning the dial, that's where you need to leave the timer go.(fans off) Wait at least ten minutes, you should see the heater come on that is near the coils. Should be a long heater that runs the length of the coils and sits under them. The thermostat is on top of the coils, left hand side.
When you get the new parts you will be able to identify them better. To get your machine running temporary again. Use a hair dryer and melt all the frost and ice on those coils. Once those coils and the surrounding area is clear of frost and ice, the machine will circulate the air normally again when its put back together. It will run fine for up to a week or so.
Then you will be right back to where you are now.
If you have anymore questions please ask. Thanks Again, for using JustAnswer.com!