Wallingford has connecting trains to New York City, so if you can get from NYC to Wilmington, then yes.
No. The best you can probably do is go from Wallingford to New York, then New York to Raleigh NC. From there you could probably take a Greyhound to Wilmington
As said above by Miguel, you can go to Amtrak.com or call 1-800-USA-RAIL and get a ticket from Wallingford, CT (WFD) to Wilmington, NC (WMN). There isn't a train that goes there, but Amtrak offers connecting Thruway Service which usually is done by Greyhound but sometimes is a local carrier. That bus ride is 3:45 hours though :/
not sure what station you are coming from but the lines that run to Wallingford, CT is Amtrak and CT Rail
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