Things are improving on the DNS side, but their website is still having problems. They've apparently posted a message about the outage on their website, but I've been unable to load the page.
They posted a brief message on their Facebook page:
Network Solutions is experiencing a Distributed Denial of Service (DDOS) attack that is impacting our customers as well as the Network Solutions site. Our technology team is working to mitigate the situation. Please check back for updates.