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Unfortunately you have a sealed system problem. This is not something you can fix yourself if the chill plate is not getting cold enough to freeze the water. You'll need a technician to come out and check the freon pressure because you either have a freon leak, the chill plate has popped internally so the freon doesn't flow properly (happens on these Kitchen Aid units), the hot gas valve is stuck partially open, or the compressor itself is just not working properly. Those would be the options but you really need to check the freon pressure and tap into the freon system to know exactly which issue you have.
No, this is not an issue you can fix yourself whatsoever. It requires certification to work on the freon system and about $1500 in tools/torches. As for servicers in your area, I'm out of Colorado so I wouldn't know who is in your area, but you can call Whirlpool who owns Kitchen Aid and see who is authorized in your area. Their number is *****
Hello again. I'm just following up because I haven't heard back from you and I see this question is still open. Is there anything else I can help you with?
I can not control what needs to be done to fix the issue and this is not something you can fix yourself as I stated before. You need a technician to come out---there is nothing you or I can do about that.