jaydawg55

Re-verify the Fallout 4 game files with your Steam client. If the original game files are messed up, it will prevent the game from launching. If Steam finds missing files it will try to re-install them. Don't try to launch the game until this process is completed. The same goes for New Vegas if you want to play that game with mods as well.
 
Don't use F4SE with Fallout New Vegas. F4SE is made for Fallout 4 not New Vegas. They are different games that use different game engines. New Vegas has its own script extender you can add if you want to play a modified version of that game.
 
Did you successfully launch each game (Fallout 4 and New Vegas) from Steam before using MO2 or Vortex to add mods to them? Don't mess with mods until you have the vanilla game launching properly from the Steam client.
 
You could also have errors in your Vortex set up. Read the Vortex Knowledgebase to verify if you have installed Vortex correctly -- with special attention to how to launch games that use script extenders. YouTube has videos showing how to install Vortex and MO2 so they will work with your games. I recommend the videos made by Gamer Poets.
 
While many players are eager to start modding their games (I know I was), it does require a bit of study to get started correctly. Don't give up.

This error is most likely a connection problem with the Steam servers. What game are you trying to play?

Did you check the Knowledgebase for how to install Vortex? Since you deleted it, you are doing a new install when you re-install it. Follow the instructions in the Knowledgebase. Here is a link that will launch it in your web browser:
 
Getting Started with Vortex | Modding.wiki
 
If you want to Vortex on the same drive as you game(s) -- and it is not drive C -- you might want to use the installer for custom install location. Here is a link to the Vortex webpage:
 
Vortex at Modding Tools - Nexus Mods
 
Putting Vortex on the same drive as your game(s) may not be necessary. Browse the wiki to see what your options might be. I have games installed on two different drives (C+D). I have not tried to add mods to any of my D drive games yet. So, it might be a problem that I am not aware of.
 
Have fun!

Short answer: You need to install the updated mod first and then delete the older version.
 
Details:
 
1. In Vortex on the Mod tab, on the top menu bar find the 'Check for Updates' button and push it.
2. Vortex will search Nexus to identify which mods in your list have an update. Have a lot of mods? This can take a while to get done. Coffee?
3. When the search is finished, find the column heading called Version. Click the dropdown and select 'Update available.'
4. A filtered list appears showing just mods with updates to install. Under the Version column is a cloud or download icon for each update.
5. Click a download icon and Vortex will bring up the Nexus Files page for that mod. Click the Nexus download button to start the download.
6. Vortex will alert you when it is ready to install. It will prompt you to update just the current profile of the game or all profiles. I usually choose all.
7. Usually Vortex pairs up installed and updated versions of the mod in a small dropdown menu. Select the minus sign next to the old version.
8. Vortex will show you a confirmation menu about deleting the old version. Be sure to click 'Delete archive' or the old art/audio files will remain in place.
9. Repeat this process for each mod to be updated.
 
Special Cases:
 
1. Sometimes Vortex will alert you to mod conflicts when you are installing an update. Follow the same process as installing a first-time mod.
2. Sometimes the conflict is between two versions of the same mod (old vs update). Filter on Mod Name and Remove the older version.
3. Sometimes Vortex does not Remove the old version but leaves it as 'Uninstalled.' I tell Vortex to Remove these mods.
 
I don't know why these special cases occur. Possibly, I am not using Vortex exactly the way I should. For SSE I have 575 mods installed, so I might be trying to get Vortex to do too many things at once.
 
The Vortex Knowledge Base or YouTube might have more information for you with pictures or video.
 
Hope this helps you.