You may need to ensure Tls1.2 is enabled for SCHANNEL in the registry. Start at this key:
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\SecurityProviders\SCHANNEL\Protocols\Tls12\Client
Create it if it doesn't already exist and make sure there's an Enabled dword set to 1. Also, any changes to the SCHANNEL configuration won't take effect until you restart the computer.
Next, check that .Net is configured in the registry to use strong cryptographic protocols:
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v2.0.50727]
"SystemDefaultTlsVersions" = dword:00000001
"SchUseStrongCrypto" = dword:00000001
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\.NETFramework\v4.0.30319]
"SystemDefaultTlsVersions" = dword:00000001
"SchUseStrongCrypto" = dword:00000001
Then this line in your PowerShell should actually be effective:
[Net.ServicePointManager]::SecurityProtocol = [Net.SecurityProtocolType]::Tls12
But, as I indicated in a comment, you really should do whatever you need to get to permission to upgrade the server.
Windows Server 2008 R2 is fully end-of-life, and has been for several years now. This means it hasn't had any updates in that time... not even critical security patches, in spite of multiple active critical-rated CVEs. It's dangerous and irresponsible to still be using it; lawyers might use phrases like "gross negligence".
all patches have been applied...
I should hope so, as there haven't been any new patches released in several years.
The minimum safe version to be using today is Windows Server 2016 (2012 R2 also reaches end of life in less than a week.) This is the kind of thing worth finding a new job over, as you don't want to the be one held responsible when (not if) this thing is breached.