Launcher is closing on its own

No idea why this is happening.

We don't either, because you have given 0 details as to where even to begin to help you.

I double click on the icon, it asks for my login and password. I scroll down and click 'Accept'. Then the launcher closes.

Running as administrator does not help. Any ideas?

General issue fixes:

Run a file check from the EQ Launcher
(HOW?
Validate Game Assets through the launchpad

Run the LaunchPad and log in, but do not press play.
Click on the Advanced Tools icon (looks like a gear) in the lower left and and choose Validate Game Assets.
Press the green Validate button to have the LaunchPad check your game files and download any missing or corrupt files.)

Right Mouse button Click the EQ Icon, select Properties then compatibility then put a check in the box for "disable full screen optimizations" hit apply then run as administrator the first time you log in

Download & install a fresh copy of Direct X 9c
(LINK 1 - https://www.microsoft.com/en-us/download/details.aspx?id=8109)

Download & install the latest C++ runtimes
(LINK - https://support.microsoft.com/en-gb/help/2977003/the-latest-supported-visual-c-downloads)

Check what Graphics hardware you are using & uninstall the old drivers & re-install the latest WHQL drivers for it or a new copy of the current drivers if you already have the latest ones.

Over-bright graphics with 2.0 shaders on:
NVidia Cards - Turn off antialiasing gamma correction from the NVidia Control Panel.

Connection issues:

Power cycle your router & modem -
Switch off for 60 seconds then back on.

Add launchpad.exe & eqgame.exe to the exceptions or white-list for your anti-virus & firewall - especially if you are using Windows Defender as this is known to often block connections to EQ.

Reset your Internet Options:
Even if you use Firefox, Google Chrome or another web browser to surf the internet, the LaunchPad runs off of Internet Explorer settings. Follow these steps to reset your Internet Options which may improve LaunchPad performance.

Go to Start, then your Control Panel.
Click on Internet Options.
Click on the Advanced Tab.
Click on Reset.
Check the box Delete Personal Settings, and then OK.
Go back to Internet Options to the Advanced Tab, scroll down to Security and un-check "Check Server Certification Revocation" and "Do Not Save Encrypted Pages to Disk".
Click OK.

Clear the LaunchPad Cache
Navigate to the directory of the game you are trying to play and open the launchpad.libs folder. Delete the launchpad.cache folder and relaunch the LaunchPad again.

Flush DNS (reset internet connection)

Navigate to the desktop. (From Home, tap or click the Desktop tile).
Right-click the Start button (the Windows logo in the lower-left).
Choose Command Prompt (Admin).
When asked whether to allow Command Prompt to make changes to your computer, select Yes.

Note: If you are asked for an administrative login, you will need to contact your system administrator.
Type "ipconfig /flushdns" and press Enter.
Type "ipconfig /registerdns" and press Enter.
Type "ipconfig /release" and press Enter.
Type "ipconfig /renew" and press Enter.
Type "netsh winsock reset" and press Enter.
Restart the computer.

I would love to do all of this, but the launch window won't stay open long enough for me to do any of it. About a second after I enter user/pw and hit 'I accept', the window closes.

Yes, they changed it a while back where you cannot validate from the first screen on the launcher. You have to go past that first screen where you enter your name and pw. And then on the second screen where the big play button is you would have the option to validate files. And that is why you cannot do that step. It closes before that.

Personally I would do the direct x 9c download linked above since it is the easiest and usually help with the launcher doing the instant close. Sometimes EQ just doesn't like the latest version of Direct X and wants that one installed also.
Download & install a fresh copy of Direct X 9c
(LINK 1 - https://www.microsoft.com/en-us/download/details.aspx?id=8109)

And then go on to the rest of the troubleshooting

ok, I am down to clearing the launchpad cache. It will not let me do this. Says the folder or a file in it is in use by another program.

Reboot your PC and do this without starting EQ - if you still get that message add the entire EQ directory to the exceptions list of whatever Anti-virus you have.

If it is still happening after that you may need to do a "clean boot" before trying.

Clean boot how to - https://support.microsoft.com/en-us...-windows-da2f9573-6eec-00ad-2f8a-a97a1807f3dd