Thank you for using Just Answer. I hope that I can assist you. Please ask any follow up questions that you may have.
Here are the steps that you can take.
1) See if the computer repair company will send you an email or other written statement that the PC needs a motherboard and the costs. (I know that you have tried this, but try again - one last time).
2) Don't worry about getting a repair estimate knowing that you are not having it repaired. This happens all the time and is part of the business. There is not anything wrong with doing it it is perfectlly Okay and on the up and up.
3) Send a letter to the extended warranty company that if they still refuse to make the repair you will file a complaint with your state's Attorney General's Office of Consumer Protection and the FTC for unfair trade practices in failing to honor the extended warranty.
4) Send a copy of this letter to the Credit Card Company's Office of General Counsel. Make sue you put the CC on the letter.
You can get the address from the credit card company or by googling "General Counsel" and the name of the credit card company.
The warranty company will almost certainly relent after steps 3 and 4.
I know that it is frustrating to have to jump through hoops to get what you are entitled to. But sometimes we just have to go through this with some of these companies. They are counting on people just giving up.
Please do not forget to rate me - click the five stars. It adds nothing to your costs but it heps me greatly. Plus it is good Karma for you. Thank you.