Power off the router. Wait awhile. Power it back on. Wait until all the lights are lit up properly.
It will take a while.
Restart the computer.
Start up in Safe Mode
Safari > Preference > Advanced
Checkmark the box for "Show Develop menu in menu bar".
Develop menu will appear in the Safari menu bar.
Click Develop and select "Empty Caches" from the dropdown.
Try troubleshooting extensions and third party plug-ins.
From your Safari menu bar click Safari > Preferences then select the Extensions tab. Turn that off if there are any installed. Quit and relaunch Safari to test. If that helped, turn extensions back on then uninstall one a time to test.
If it's not an extensions issue, try troubleshooting third party plug-ins.
Back to Safari > Preferences. This time select the Security tab. Deselect: Allow all other plug-ins. Quit and relaunch Safari to test.
If that made a difference, instructions for troubleshooting plugins here.