Did suddenly get same problem yesterday. Both SL viewer and Firestorm shutting down before I culd press login.
I tried unninstall, reinstall, deleting cache...all the standard sugestions, and none of them worked.
So I did go into eventviewer to see if I could find any clues to the problem there. There I found this errror:
Error programpath: D:\Second Life\SL vIEWER\SecondLifeViewer\SecondLifeViewer.exe Error modulepath:: C:\PROGRA~2\Raptr Inc\PlaysTV\ltc_game32-114279.dll
The fix for me was unninstall Raptr, and remove all its parts, deleting folder completly. Also did a regestry clean up after to remove all trash left by this program. I think Raptr is bundle software that comes with AMD software/drivers.
Disable Raptr might be enough: https://steamcommunity.com/app/206190/discussions/0/611696927931005910/