Miles, did you have a transformer blow up outside? If not I doubt most homeowner policies will cover the failure of electronic devices UNLESS it is caused by outside forces like that or something such as a flood, fire, etc. A homeowners policy doesn't cover routine failure of electronics devices, appliances, etc.
"Was this a catastrophic failure or just the old capacitors giving up?" Impossible to tell from here. Find a good shop and get a repair estimate and go from there.