2002 Buick Century Stall when cold

Hi gang,
My 2002 Buick Century stalled after first start in ther morning last week, but the rest of the day is fine. I brought it the the dealer and they quote
me $800+ repair, the parts they said I need are PCM - 12209614 and Harness - 10447429 (rear O2 sensor?). I have the GM Guard extended warranty, you think they will cover it? Any ideas and comments are welcome
Thanks Kenny
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The policy lists coverage, the pcm is covered on the emissions warranty, for 7/70. Check your warrantty booklet on that.

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