If you can’t download vSphere Client 5.1 Plugins (eg vShield), and can’t use the search in the client because of:

An unknown connection error occured. (The request failed due to an SSL Error. (The request was aborted. Could not create SSL\TLS secure channel.)

And https://kb.vmware.com/selfservice/microsites/search.do?language=en_US&cmd=displayKC&externalId=2114357 is of no help (you already allow all SSL.Versions), and your SSL certs don’t appear to be broken or expired, then you’ve probably been bitten by some recent changes in a windows update that’s evidently changed some defaults around the minimum DH key size.

Create the following key; everything will start working immediately (you’ll need to re-enable any disabled vSphere Client plugins) as you will start permitting 512bit DH keys.

[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\KeyExchangeAlgorithms\Diffie-Hellman]
"ClientMinKeyBitLength"=dword:00000200

You should consider upgrading to newer versions of vSphere, but then if we all sat around doing things as complicated as that, we’d not have time for any actual work, would we.