Ok. You're clear but not clear enough...
First... whenever you make a DNS change... it takes roughly 72 hours for changes to take effect and be reflected. (24 hours in many cases for MOST of the internet and bigger ISPs to pick up and reflect new changes) ...knowing that, that's why you were still seeing the old site analytics still counting the next day and why you saw it stop mostly around 3 days.
Secondly... google is pretty darn quick.
This is where it gets sketchy and you still need to provide more info:
- If you manually refresh the website does the new site load? (could it be a caching problem with your browser or even your network's cache)
- Have you performed a WHOIS on your domain to see if the changes are reflected? (http://www.internic.net/whois.html
- Have you checked the DNS records in your godaddy account since you noticed this problem?
- Have you confirmed this on another computer? In an entirely different location with hopefully a different ISP? With your cellphone even...? How about any out of state friends/family since they are routed differently?
I would suggest RENAMING your index page on your old site to something like index_old or something like that... see if you are actually seeing that change immediately since you should then see some type of 404 if that server is configured properly. At least at that point you could say the DNS needs looked at again. If you don't see the 404 page then I would suspect some sort of page caching locally on your pc, or on your network's servers(not your ISPs network). If it's not that... report back.