My domain name expired and although I was working with my Network Solutions to update my information somehow they let my name go and it was picked up by NVS Corp. At this point I can not get any information from anyone as to how I can purchase it back. My question is I spent thousands of dollars on the actual web site...so where is the web site now?
You only lost your domain name, not your website. Your website is right where you left it. You just can't see it right now because your domain name doesn't resolve to it anymore.
I don't know for sure but I suspect NVS Corp is one of those companies that buys expired domains solely for the purpose of monetizing their existing traffic. My guess is you will not be able to buy your domain back from them. But that's just speculation.
What you need to do is purchase a new domain, make sure you don't have any outdated or incorrect information when you register it, and point that to your website. Within an hour or so your website will be visible again.
This is going to kill your SEO as all of the incoming links to your website will be outdated. You will need to contact the sites where you have links and ask them to update their links to your website with your new domain name.
You don't need to simply give up your domain name! There are dispute resolution avenues available to you. Usually, you want to contact the registrar you were using and discuss disputing this transfer.
My domain name was transferred without my authorization. What do I do?
If you believe that your domain name was transferred to a new registrar without your authorization or consent, please contact the original registrar. Disputes between registrars over alleged violations of the Inter-Registrar Transfer Policy may be initiated by any ICANN-accredited registrar.
How do I find out why my transfer request was denied?
If your current registrar denies a transfer request, they are required to provide you with the reason. Contact the registrar for assistance. See above for the circumstances in which a registrar may legitimately deny a transfer request.
My domain has been transferred to some other registrar without my knowledge, and now it shows someone else as the owner. What do I do?
A registrar may only initiate a transfer if it has obtained a completed Form of Authorization (FOA) from either 1) the registrant or 2) the administrative contact for the domain. The registrar must be able to produce a copy of this documentation when it is requested. Failure to do so is grounds for reversal of a transfer in the event that a complaint is filed under the Transfer Dispute Resolution Policy.
Thus, the first step should be for your previous registrar to request from the new registrar a copy of the form used for authorizing the transfer. The registrar can then proceed with initiating a dispute as appropriate. Contact your previous registrar for assistance.