Domain Controller

This is a very common issue you should never use the same internal domain name as external.  Can you put the output of ping and nslookup in the comments below.  You may need a host entry as you can not change the @ address on your domain to point to a non AD controller.

I'm not quite sure if I'm understanding the details in your post. However, you need a host entry on your internal DNS server pointing to the EXTERNAL IP address of the website in order for this to work.  It's pretty straightforward: just add an "A" record on your internal DNS server to "www" (or whatever alias you're using for your website) and point it to the external IP address of the website.  If that doesn't work, then there's probably some sort of redirect going on at GoDaddy and you might have to check with them.

Website just stopped working internally after we moved hosting from hostgator to godaddy. Ping correctly responds with static ip address. Nslookup gives  me correctly my DC ip address and correct static ip address of the website.

I cleared cache on my computer and flushdns as well.

I've had this problem with other websites hosted using Word Press, but I have to confess that I don't quite understand the exact principles behind what fixed it and they did not take the time to explain. I had to coordinate with an outside web designer and they gave me a different IP address that worked (i.e., it wasn't the same IP address that was used externally to get to the website).  I'd suggest calling GoDaddy and find out if they can help you out.

I already have A record. so when I ping the website it returns the correct IP address . website does not work internally through the web browser.

Do I need reverse lookup as well?

Godaddy mentioned since the website is working externally they will not be able to assist further.

I did dnsflush and reconfigure.

When I try to browse the website it comes up with prompt for username and password.

Do you have any web filtering or proxies that need to be updated?
Are there any other resources that the website is pulling that need to have DNS records added too? (Like images.example.com or js.example.com)

I dont believe we have any other resources that need to have DNS records added.

I tested index.html page on godaddy and it works inside LAN. But wordpress website prompts users for username and password. I dont know what username and password it is looking for. We disabled all the plugins on the wordpress website.

Also when I ping www.example.com it will reply with correct IP address however if I ping just example.com it replies with ip address of the internal DNS server.

I had them redirect the web URL to https: