Whether you can use an existing backlink profile for a new web project under the available domain depends on whether the link target of incoming links can be reconstructed. In order to analyze which content was provided under a domain in the past, you can find out on the Internet Archive Backlinks have no value if they lead to nowhere and this can even have a negative impact. They are possibly redirected to similar subpages or homepages using 301 redirect. In this case the most part of the link’s power is lost.
Also with the domains, a name which can be cheap for one can be worth gold for the other. Permute the letters in your domain name and try contacting and eventually selling out to organizations that run under those names or contain the letters within. Companies would be keenly interested in buying out the domain names that matches the product's name. Hint : Look for companies on LinkedIn