What I did:
I installed a fresh copy of the launcher. I tried two separate distributions (two separate launchers), both the latest version. They both support Minecraft 1.14.4.
I assume they both are using <user>\AppData\Roaming\.minecraft as the game directory.
I installed forge-1.14.4-28.1.0-installer in that game directory (default).
I started the launcher.
I selected the Forge profile. Edit profile. Selected to use version: release 1.14.4.
Selected D:\Java\jdk1.8.0_221\bin\javaw.exe for the Java executable explicitly, since I also have a JDK 11 installed.
(When I select Java 11 I have to remove -XX:+CMSIncrementalMode from the JVM args to get Minecraft started, with or without Forge installed).
I save the profile and start Minecraft (play).
No Mods button.
?