There's an official process for forcing the release of domains which use invalid Whois data:
Step 1: file a report
You should first file a 'Whois data problem report'. You can do this in two ways (pick one or both):
Using InteNIC's Whois data problem report form.
By searching for the domain with GoDaddy's Whois lookup service, scrolling to the bottom of the right-hand column, and clicking 'report invalid whois.':
Step 2: wait it out
Once it's reported, GoDaddy have an obligation to attempt to contact the registrant to ask them to correct their registration data. They supposedly have a full-time team whose job it is to do this. GoDaddy first charges the registrant a fixed fee of about $10 for not having kept the Whois data up to date (source), then emails them to explain the steps that the registrant needs to take to correct their data. From here, one of two things will happen:
- The registrant will correct their Whois data, and you may be able to contact them.
- The registrant won't reply. This is good news for you, because you now have a genuine chance to snag the domain at a fraction of the cost you might have agreed were you able to contact the registrant directly.
Step 3: get ready to catch the expiring domain
If the registrant's phone number on the account is unreachable or the emails that GoDaddy send trying to contact them bounce, they 'suspend' the domain, which places a public suspension notice on the URL, and send the registrant an email asking them to contact GoDaddy's support team. If no further contact is made within a fixed period (about 60 days), GoDaddy will terminate the domain, which forces it to expire and become available for registration again within 75 days.
Registering a domain that's in the process of expiring is harder than it sounds, because several companies (including GoDaddy!) monitor expiring domains and re-register good names straight away to sell or sit on. You could use GoDaddy's backordering service (as soon as you've reported the incorrect Whois record) to attempt to become 'first in the queue' should the domain expire. Because the domain's registered through GoDaddy, this should be enough to acquire it assuming no-one backordered it before you, but you may wish to follow the advice presented in this article and use a 'drop catching' service, who try to register the domain for you should GoDaddy's backorder service fail to take effect for some reason.
I have successfully registered one domain using the process described above. It took about 150 days from start to finish, during which time I had completely forgotten that I'd backordered the domain and registered a different one instead! It's a lengthy process, and you may wish to simply pick a different name.
In summary, when a domain is still active and the Whois data is valid, your only chance of snagging it is to contact the registrant. But when the Whois data is invalid, it actually makes domain acquisition a tiny bit easier. It's one of the main reasons you should keep your own Whois data up to date, or use a Whois privacy service and be sure to pay attention to all incoming emails from your registrar, so you don't mistake ones needing action for marketing email.