Hi Brian,
You may want to try the following steps and see if they prove to be of any help to you:
1] Launch standalone ArcCatalog and check if the issue is reproducible.
2] Open Windows Explorer and go to the following path on your computer. If you have a 32-bit system the path will exist at C:\Program Files else the following location:
C:\Program Files (x86)\Common Files\ArcGIS\Desktop10.2.2\Configuration\CATID
If the CATID folder exists, it will contain files which have an ECFG extension. These files initialize 3rd party extensions that may exist on your computer that were installed for previous versions of ArcGIS Desktop. If the CATID folder exists, rename the folder as CATID_old. This will disable the extensions.
3] Try logging onto your machine with a different user profile and see if the issue persists. If it doesn't, it might be a case of corrupt user profile and you might have to contact your IT guys.
4] Try registering the system toolbox through ArcCatalog's Search Options. Go to Search Options drop-down and click on Search Options >Index tab > Click on Add and navigate to C:\Program Files (x86)\ArcGIS\Desktop10.2\ArcToolbox\Toolboxes. Now click 'Index New Items' > Apply > Ok.
Launch ArcMap and try searching for tools.
I hope this helps!