Hello, my name is Ben and it is my pleasure to assist you with your question today.
When you booked your tickets you agreed to be bound by the booking terms and conditions of Ryanair, which you can find here:
Article 10 deals with the right to receive a refund and states that a refund will be issued only in the following circumstances:
In addition, there is a relevant clause found in Article 3, which says that:
"In the event of serious illness (or death) of a Passenger making it impossible to travel, the reservations of the affected Passenger and of persons travelling on the same booking reference may, at our discretion, be refunded or, as appropriate, modified by our waiving any restriction or fee on changing flights upon suitable documentary evidence produced to us in advance of the date of travel."
Whilst you have tried to request a booking, all you can do is go via the formal channels in the airline. Unfortunately not every company will have the level of customer service we would expect, or like them to deliver and this is something that consumers can often do little about.
At this stage the best you can do really is continue to contact them via the official channels and stress the importance of resolving this as soon as possible, providing whatever necessary details you believe are relevant to show what you are dealing with here.
If you get nowhere with your current attempts and the flight date has passed then you can consider tasking this down the formal legal route. Whilst not ideal, it may be your only option in the circumstances. That is why it is important to keep copies of all documents and a diary of all events in case it is need in the future to show that you had made all efforts to resolve this via the proper channels.
Please let me know if this has answered your query or if you need me to clarify anything else for you in relation to this?