and also updated the A record but it still did not work.
When you're moving to a third-party host, it is normally enough to update your name servers. Do you know why GoDaddy is telling you to modify the A record as well? To what exactly are they asking you to change it?
Could you show me the exact instructions they gave you?
Have you tried just updating the name servers and not touching the A record?
I got a message in my WordPress account that said to change the nameservers to ones that end in wordpress.com. That did not work either.
That message is intended for users with a WordPress.com site, not for those who are using another host.
Do the nameservers need to be GoDaddy's or WordPress'?
If you're keeping your site hosted here at WordPress, they should be the WordPress name servers. If you're hosting your site through GoDaddy, they should be GoDaddy's name servers.