Now this is a very strange thing. I installed Quake 1, and the game didn't fully launch after start. Instead, it stopped at I think some sound information, and the Screen was clearly flickering! Even after force-quitting the unresponsive program, the flickering persisted. This is even more strange as my LCD should be incapable of flickering, as it's a flicker-free Technology. It must have run at 30 Hz per second! In my Nvidia drivers settings, however, I still had 60 Hz. Changing resolutions or restarting the computer didn't help. The driver settings didn't let me change the refresh rate, it was fixed at 60 Hz, although I couldn't really believe it. The flickering only stopped after I think I switched to my administrator account and back, I'm still not sure. Below my config.cfg of the Quake game. Are there other alternative interpretations or some diagnostics I can run? I'm somewhat afraid of running the game again...

Thanks.

Below config.cfg (Id1 folder), only things changed after the incident was the resolution.

bind "TAB" "+showscores"
bind "ENTER" "+jump"
bind "ESCAPE" "togglemenu"
bind "SPACE" "+jump"
bind "+" "sizeup"
bind "," "+moveleft"
bind "-" "sizedown"
bind "." "+moveright"
bind "/" "impulse 10"
bind "0" "impulse 0"
bind "1" "impulse 1"
bind "2" "impulse 2"
bind "3" "impulse 3"
bind "4" "impulse 4"
bind "5" "impulse 5"
bind "6" "impulse 6"
bind "7" "impulse 7"
bind "8" "impulse 8"
bind "=" "sizeup"
bind "\" "+mlook"
bind "`" "toggleconsole"
bind "a" "+lookup"
bind "c" "+movedown"
bind "d" "+moveup"
bind "t" "messagemode"
bind "z" "+lookdown"
bind "~" "toggleconsole"
bind "UPARROW" "+forward"
bind "DOWNARROW" "+back"
bind "LEFTARROW" "+left"
bind "RIGHTARROW" "+right"
bind "ALT" "+strafe"
bind "CTRL" "+attack"
bind "SHIFT" "+speed"
bind "F1" "help"
bind "F2" "menu_save"
bind "F3" "menu_load"
bind "F4" "menu_options"
bind "F5" "menu_multiplayer"
bind "F6" "echo Quicksaving...; wait; save quick"
bind "F9" "echo Quickloading...; wait; load quick"
bind "F10" "quit"
bind "F11" "zoom_in"
bind "F12" "screenshot"
bind "INS" "+klook"
bind "DEL" "+lookdown"
bind "PGDN" "+lookup"
bind "END" "centerview"
bind "MOUSE1" "+attack"
bind "MOUSE2" "+forward"
bind "MOUSE3" "+mlook"
bind "PAUSE" "pause"
joystick "0"
m_side "0.8"
m_forward "1"
m_yaw "0.022"
m_pitch "0.022"
sensitivity "3"
lookstrafe "0"
lookspring "0"
cl_backspeed "400.000000"
cl_forwardspeed "400.000000"
_cl_color "0"
_cl_name "player"
_snd_mixahead "0.1"
bgmvolume "1.000000"
volume "0.7"
viewsize "100"
_windowed_mouse "0"
vid_stretch_by_2 "1"
vid_config_y "1200"
vid_config_x "1920"
_vid_default_mode_win "3"
_vid_default_mode "0"
_vid_wait_override "0"
vid_nopageflip "0"
_config_modem_hangup "AT H"
_config_modem_init ""
_config_modem_clear "ATZ"
_config_modem_dialtype "T"
_config_com_modem "1.000000"
_config_com_baud "57600.000000"
_config_com_irq "4.000000"
_config_com_port "1016.000000"
saved4 "0"
saved3 "0"
saved2 "0"
saved1 "0"
savedgamecfg "0"
gamma "1.0"
crosshair "0"
vid_conheight "400"

Which version of Quake are you using? From the description I take it you're starting it using the "Launch Quake" shortcut, is that correct? In this case you are using DOSBox to play the DOS version. On GOG Quake also comes with the official ports GLQuake and WinQuake.

Unfortunately, I'm not tech savvy enough to directly help with your issue. I can only advise you to use a different version of Quake, as from my experience the DOSBox version doesn't run satisfyingly, anyway. You can try the winquake.exe in the Quake folder, otherwise it's usually just a case of downloading a different executable file, putting it in the Quake folder and starting it, so really straightforward.
The most popular choice would be Quakespasm, but if you're interested in playing Quake exactly the same way it would be through DOSBox except for the technical problems, I can recommend the WinQuake port of Fitzquake Mark V. If that's would you want I suggest you take a look at the "Making Quake look most retro..." thread where I added everything you need to know to set it up, it's really quick process :)

I used GOG Galaxy to install and launch Quake. I had glquake.exe running.