Hi Peter,
The only time the "Obtain DNS server address automatically" is greyed out is if you have selected a
STATIC IP ADDRESS, in other words you have selected
NOT to use "Obtain an IP address automatically". If you do this and select a Static IP Address, you are electing not to have your IP address for your computer assigned by the DHCP in your router/gateway. Without DHCP to assign this address to your computer,
YOU must manually input your 2(two) DNS servers; Primary and Alternative DNS servers. In your case, the Preferred DNS server = 8.8.8.8 (google) and the Alternate DNS server 192.168.0.1 (your router). This also
GREYS OUT THAT OPTION, since you cannot use the DNS automatic server assignment without also using the DHCP auto-IP addressing scheme in conjunction with it.
This is the old IP addressing scheme used 20 years ago by just about everyone, and it has more disadvantages than advantages in today's home networking environment. One of the advantages is *and this is more important for peripheral devices such as printers and webcams* is that the Static IP address you assign to your computer will never change. If you are using DHCP addressing on other computers and devices on your home network they will avoid the IP address you assigned manually to your computer, and work around it so to speak. So, if your computer's IP is for example, 192.168.0.22, and you are adding other devices with DHCP in a range of 192.168.0.2 to 192.168.0.50, you have 49 device IP's that can be selected for this new device in that range. For example, a new laptop added could be 192.168.0.21 or 192.168.0.23, but
NOT 192.168.0.22 as that has been manually assigned by you to your computer as above, and can never be used by any other device on your network. Of course, this is not entirely intuitive and that may be confusing you.
The deal is that modern routers prefer you to use DHCP coupled with DNS for automatic addressing of IP's to your computers and peripheral devices on your LAN. The old-school option of manual IP addressing is still available for older networks or for people who have not figured out how to do it with the newer more modern scheme, or have really old routers still running their home networks etc.
Using DHCP and DNS also allows you to use advanced addressing schemes such as WINS, Proxy Server, RIP protocol, and VPNs. Few home users will ever use these functions unless their work network Administrators or University Administrators provide them with these special settings to access their networks remotely from an employee's home or a student's home or dorm.
This is probably more information than you wanted, but it a nutshell you are trying to use DNS automatic addressing of servers without DHCP auto-IP addressing which is not possible.
I recommend that if you want it to work correctly, you should reverse your Primary DNS and make that 192.168.0.1 (router) and use the 8.8.8.8 (google) as the Alternate DNS.
Enabling DHCP and DNS in this fashion lets your router control the IP address assignment to your computer and only if your router doesn't respond it will try to go out to the Internet and use Google's DNS to complete this task. It would actually be best, if you did this:
ENABLE DHCP
ENABLE DNS
PRIMARY DNS: 192.168.0.1
ALTERNATE DNS: 192.168.0.1
OR this
ENABLE DHCP
ENABLE DNS
PRIMARY DNS: 8.8.8.8 (Google)
ALTERNATE DNS: 8.8.4.4 (also Google)
Either of these methods will provide a better DNS resolution path than how you have it. If neither of these work, and you have more than one of your computers set to each of these configurations in turn with no love, your Router is out of date and most likely needs to be replaced with a more modern one.
The fact that you are mixing Static IP addressing with DHCP indicates that you have a really old router and are trying to make a decades-old addressing scheme work on your home network which is completely unnecessary with todays networks and ISPs.
Hope that helps,
<<<BIGBEARJEDI>>>