When I click play off of steam, it will bring up a launcher for me to install, but everytime i click install it just closes the launcher and brings it back up.

1. Run Directly from Game File

Navigate to your Steam installation (By default C:\Program Files (x86)\Steam)

Then goto the SteamApps\common\skyrim directory

From here just run TESV.exe directly.

If it's missing, go to step 2.

2. The game file TESV.exe or any other file is missing.

In Steam, right click Skyrim

Select Properties

Goto Local Files tab

Click "Verify Integrity of Game Cache"

It should download all broken/missing files.