Water doesn't fill in ice tray seems that the line is frozen

Hi and welcome to FixYa, I am Kelly. If the fill tube at the top rear of the unit is full of ice this is usually caused by the inlet water valve pssing water when it is supposed to be shut off. Here is what you can do to check and see if the inlet water vale is bypassing water when it should be closed.
1. On the back of the unit where the small plastic line connects to the fill tube that gouse from the rear of the cabinet to the ice maker remove the small plastic line. Plate the end of the line in a bucket or large pan for 8 to 10 hours with the ice maker OFF.
2. At the end of the period where you have the removed line in the catch basin / pan or bucket, check for water. If there is water in the catch basin the inlet water valve has failed internally either from age or debris on the diaphram seat.

Since you did not provide a model number, I can not pass you a source for replacement parts or EXACT troubleshooting procedures. However here is a manual that will assist you in trouble shooting:
http://adcxns1.whirlpool.com/Service/SrvTechAdm.nsf/2cd44500d572193285256a45004fd9d6/8527f904cc8ea8cd85256b5800672333/$FILE/4322658A.pdf

If your ice maker does not have the optical sensors use this link for ice maker troubleshooting:
http://www.american-appliance.com/catalog/newsdesk_info.php?newsPath=12&newsdesk_id=34

Here are 2 links for replacement parts: (model number is required)
http://www.appliancepartspros.com/

http://www.searspartsdirect.com/

Here is one of 2 types if inlet water valve: (example only as no model number to reference)
http://www.appliancepartspros.com/Appliance-Parts/WHIRLPOOL-Dual-water-inlet-valve-kit-item-number-AP3085178.aspx

Thanks for choosing FixYa,
Kelly