While there are many potential reasons why your Manjaro installation doesn't boot to a desktop, the primary reason is that the graphics drivers haven't loaded correctly so your login/display manager (DM) doesn't start. This is why you get a "black screen" or stuck at an
[ OK ] Started some service
The normal reason for this is that you have the incorrect driver version for the kernel. This happens when the mirror you are updating from is not fully synchronised and so has different sets of packages in [core] and [extra]. This means the driver extramodule package in [extra] has been built for a different kernel point-release than that in [core].
The first thing to try
Switch to a text console with CTRL+ALT+F2, log in with your normal username and password, then run a full update:
sudo pacman-mirrors -f3 sudo pacman -Syyu
The first command will refresh your mirror list, picking three of the most recently updated mirrors (so those mirrors will all be up-to-date).
The second command will force a download of the current package lists, then perform an update if any updated packages are available.
If any packages were updated, reboot.
Note: If you can't log in to a text console, use a chroot instead.
The second thing to try
Log into a text console as above and run
startx. This should either start X, in which case the issue lies with your Display Manager (e.g. GDM, LightDM, SDDM), OR you will be presented with some output and returned to the console. Of particular interest are Error (EE) lines.
If you can't see anything obvious
If neither approach helps fix this issue (which the first one will in 90% of cases) then search the forum (https://archived.forum.manjaro.org/search?q=black%20screen), and, if you can't find anything, start a new thread mentioning what you have already tried.
If you want more detailed instructions
Read this thread: