Go step by step and test.
1. Power off the router. Unplug it from the wall. Wait a while.
Plug it back to the wall. Power the router on. Wait until all lights are lit properly. It will take a while.
Restart the computer.
Start up in Safe Mode.
https://support.apple.com/kb/PH18760?locale=en_US
2. Delete Caches.db
Close all windows and quit all applications.
Hold "option" key down and click "Go" menu in the Finder menu bar.
Select "Library" from the dropdown.
Library > Caches > com.apple.Safari > Caches.db
Right click the Caches.db file and select "Move To Trash”.
Close windows.
Restart and relaunch Safari.
3. Empty Caches
Safari > Preference > Advanced
Checkmark the box beside "Show Develop menu in menu bar".
Develop menu will appear in the Safari menu bar.
Click Develop and select "Empty Caches" from the dropdown.
4. Delete Cookies
Safari > Preferences > Privacy > Cookies and other website data:
Click the “Details” button.
Remove all cookies except ones from Apple, your internet service provider and banks.
5. Safari > Preferences > Extensions
Uncheck boxes beside “Enable Extension” and test.
Enable Extensions one by one and test.
To uninstall any extension, select it and click the “Uninstall” button.
6. Delete com.apple.Safari.plist file and test.
Empty the Trash.
Quit all applications.
Hold the option key down and click the "Go" menu in the Finder menu bar.
Select "Library" from the drop down.
Library > Preferences > com.apple.Safari.plist
Right click on it and select "Move it to Trash".
Close the Finder window.
Restart. Relaunch Safari.
If this doesn’t help, “Put Back” the com.apple.Safari.plist
Right click on the Trash icon in the Dock and select “Open”.
Right click on the com.apple.Safari.plist and select “Put Back”.