What you can do in this case is when you connect through SQL server management studio ( SSMS) to instance on SSMS windows select option .There you can see timeout second as 30 change ot to 90 or 180 see if this helps.
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my database engine is running and I am able to connect through DAC
If a DAC = Dedicated Admin Connection works, then also "normal" connections should work; even if the SQL Server is running in Single User mode. One difference of DAC. It uses a different IP port. Have you unblocked all required IP ports in your firewall?
You have disable temporary you firewall and try it again.
Are you using the same SQL Server instance name for your connection as for DAC?