SQL Server – Unable to Login Using SSMS and SQL Agent Failing

I have SQL Server 2008 R2 ENT insalled on Windows server 2008 R2 ENT. I am unable to login to SQL Server locally after the installation. Getting below error:

Connection handshake failed. An OS call failed: (80090331)
0x80090331(The client and server cannot communicate, because they do
not possess a common algorithm.). State 56.

The error led me to this article and I updated my DB engine to 10.50.6542.0. But still unable to login. What should I do in order to allow my SSMS to connect locally. Also the second issue is SQL agent service is not starting. It fails with below error:

Agent could not be started ( unable to connect to server (local),
SQLserveragent cannot start).

How to fix this as well? Below is my environment details:

• Windows server 2008 R2 Ent. SP1
• SQL Server 2008 R2 Ent (10.50.6542.0)
• .Net version 4.6.01055

SCHANNEL Status:

SSL 2.0: Client: DisabledByDefault = 1 Enabled = 0 Server:
DisabledByDefault = 1 Enabled = 0

SSL 3.0: Client: DisabledByDefault = 1 Enabled = 0 Server:
DisabledByDefault = 1 Enabled = 0

TLS 1.0: Client: DisabledByDefault = 0 Enabled = 1 Server:
DisabledByDefault = 0 Enabled = 1

TLS 1.1: Client: DisabledByDefault = 0 Enabled = 1 Server:
DisabledByDefault = 0 Enabled = 1

TLS 1.2: Client: DisabledByDefault = 0 Enabled = 1 Server:
DisabledByDefault = 0 Enabled = 1

Please let me know if you need any further details.

Update:

I made some progress on it. I installed ADO.NET – SqlClient (.NET Framework 3.5/.NET Framework 2.0 SP2) referring link https://support.microsoft.com/en-us/kb/3135244. I am now able to connect SQL server using SSMS locally and also able to start SQL agent service. Yipee.

But now the new issue is appearing. I can't connect the server remotely using windows authentication. I get below errors in windows eventviewer logs when I try to connect it. Also, no errors in SQL server error logs.

Log Name: System Source: Schannel Event ID: 36888
Task Category: None Level: Error Keywords: User:
SYSTEM Description: The following fatal alert was generated: 40. The
internal error state is 1205. Log Name: System Source:
Schannel Event ID: 36874 Task Category: None Level:
Error Keywords: User: SYSTEM Description: An TLS 1.0
connection request was received from a remote client application, but
none of the cipher suites supported by the client application are
supported by the server. The SSL connection request has failed.