Trying to launch Skyrim through Steam, installed, updated.
As soon as I press Play on the Skyrim Launcher, the launcher goes off and the Skyrim application stops with no effect on RAM or CPU usage.
Any ideas?

Only if you were asking about a console version would a question that omits any useful information be a more or less acceptable message. However, this is the PC forum, and there is nothing in your message that has any use for diagnostics, so the old saying will apply:

"No data in = no data out."