Be wary Eon cannot just demand anything at this point like 10 days , they have to allow you enough time to send your pc in for inspection and the result of that would be your defense, however at this stage the cost lies on your shoulders, only if you can show the motherboard failed due to surges etc then you are kinda on a losing battle, it would take hard drive evidence it was working prior to the visit through timestamps and then a report that an external electrical issue was the probable culprit, then all your costs could be claimed.
They are a big company with money for solicitors, I cannot say if what happened is their fault or just coincidence, if your computer is always plugged in permanently but just in sleep etc then a power outage can see normally warm hot components fail which isn't as uncommon as people realise, factory shut downs and machinery issues are a regular thing I deal with and basically the electronics are energised for so long, 6 months plus in some cases that when the boards finally switch off and cool down they can get component failure.