First, don't say "not wanting". Say "not able". They want to pay, but it doesn't matter, because they can't pay.
Next, sue the guy (not State Farm) for causing the accident (not for lying to State Farm).
If you sue and you win, then State Farm will pay.
But if you sue him only for lying (not for the accident), then they can't pay. In some states, if you sue only State Farm, and not him, then they can't pay.
Or continue talking about them "not wanting" to do what they can't do, and don't get paid.