Mysql closing immediately after new installation
The error (2003) Can't connect to MySQL server on 'server' (10061) indicates that the network connection has been refused. You should check that there is a MySQL server running, that it has network connections enabled, and that the network port you specified is the one configured on the server.

Start by checking whether there is a process named mysqld running on your server host. (Use ps xa | grep mysqld on Unix or the Task Manager on Windows.) If there is no such process, you should start the server. 

If a mysqld process is running, you can check it by trying the following commands. The port number or Unix socket file name might be different in your setup. host_ip represents the IP address of the machine where the server is running.

shell&gt; mysqladmin version
shell&gt; mysqladmin variables
shell&gt; mysqladmin -h `hostname` version variables
shell&gt; mysqladmin -h `hostname` --port=3306 version
shell&gt; mysqladmin -h host_ip version
shell&gt; mysqladmin --protocol=SOCKET --socket=/tmp/mysql.sock version


EDITED

Please go through the link for windows once

EDITED 2

1. Run your cmd as administrator.

2.What you will see is like this
c:\windows\system32&gt;

3.Go to your bin location by using cd..
like C:\mysql\bin(my location of bin in my computer is what you are seeing so chose yours correctly)

4.C:\mysql\bin&gt;mysql --install
  Service successfully installed.

5.C:\mysql\bin&gt;NET START MySql
 The MySql service is starting
 The MySql service was started successfully


Then last step is

6.C:\mysql\bin&gt;mysql -u root - p admin


It will ask for password don't enter anything first time because it will use blank, n just press enter you are done.

N later you can set password too...:)