Personally I would look for a new name, but it depends on what the web site is for. If you're having any type of business, I would not want to be associated with another company by name. So for that reason I would seek a new one.
Also, if you do have any type of business, you should try to get the .com TLD. It's still the most recognized.
Now, if it's just a personal site, then the .net / .org may be of use to you. I can't really say if the company that owns the .com name has a right to .net names or not. But they may have a right to their company name. I'm surprised if its' any size of a company that they haven't tied up at least the .net domain.
Bottom line, be unique on the net ...... which is getting harder to do now-a-days. 😉