NEW TO DNS (HELP!)

We have a DNS Server in our company.
Primary IP: 172.16.10.3

Secondary IP: 172.16.11.3

However, if I access the company website thru internal network. It does not work if I put both the DNS IP in the IP settings. But when i changed it to 8.8.8.8 it works fine.
What is the problem of it? Do I need to permanently used the 8.8.8.8 configured on my pc DNS settings?
Thank you