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What a tragic set of events. Yes, you can sue. Before you do that, you may want to make a claim on your insurance. They may cover you and even seek recovery of your deductible.
There is no substitute for the professional advice of an attorney who knows your case and represents you. My post is not, and may not be relied on as, legal advice and does not create an attorney-client relationship. Best wishes for a just and expeditious resolution.
Contacting your insurance company is a good starting point.
Your insurance may not cover all your damages (particularly the emotional), so you may decide to sue depending on what they will cover.
Another factor to consider is the condition of your propane tank -- especially, if it was not properly maintained as that may have increased the amount of the damage.
If you sue, remember you have the burden to prove that the wire caused all the damage and your neighbor may try to argue that the propane tank contributed to the amount of damage.