Since you’re using 192.168.* addresses, I’m assuming you just want a static address within your own network and aren’t trying to have a static external address.
Also assuming your info is correct (like the gateway address, subnet, etc.) - what is likely happening is that when you get your new static address and are no longer using DHCP, your machine is not configured to resolve DNS any more (as it gets DNS server info from the DHCP). That would be consistent with you showing as connected, but not resolving any web addresses.
You’ll have to manually set the DNS servers so your machine knows how to resolve addresses.
An alternate option would be to have your router hand out “static” addresses via DHCP. Most of the routers I’ve seen can do this. You can tell it to always assign a specific IP address to a specific network adapter (identified by its MAC address). This will allow you to stay configured with DHCP, still get DNS automatically from the DHCP server, but have a locally “static” address on your network in the event you want to run servers, etc. This is especially good for laptops (machines that join various networks routinely(, as you typically never need to change your networking settings - you just always stay DHCP - but still get a (mostly) static address on your own network.
(Different routers will call this by different terms in their control panels. Look for address reservation, static DHCP, IP address affinity, etc.)