Cannot open user default database. Login failed. Login failed for user Domain\Server$ on ASP MVC App

Hello,
I have app running on IIS 7 on Server2, it access the live DB on Server1.

I get the error below:

[SqlException (0x80131904): Cannot open user default database. Login failed.
[HttpException (0x80004005): Cannot open user default database. Login failed.
[HttpException (0x80004005): Cannot open user default database. Login failed.

I can't log in to the Sql Studio as this account cause it is a Computer.
Ive tried assigning map to my LiveDB, master, temp. No change.
I also tried adding NetworkService as a user to the server2. , no change.
Both servers are up and running, with no other issues.
Server1 was restored proir to this happening.
Both firewalls are down.
And help or advice appreciated.
Log shows unsuccesful login:-
Logon,Unknown,Error: 18456 Severity: 14 State: 40.

can you login as yourself?

Yeah, I can log in with my Domain credentials and also as 'sa' while on the machine, but I can't connect from another machine. I can see it in the login dialog, under network but comes up with Network error.

TITLE: Connect to Server

Cannot connect to SERVER2\SQLEXPRESS2.


ADDITIONAL INFORMATION:

A network-related or instance-specific error occurred while establishing a connection to SQL Server. The server was not found or was not accessible. Verify that the instance name is correct and that SQL Server is configured to allow remote connections. (provider: TCP Provider, error: 0 - The wait operation timed out.) (Microsoft SQL Server, Error: 258)


The wait operation timed out

I changed the app pool to use my ID . Fixed.

The next time you change your password,, or your account is locked, or you get married and change your name, or you are let go from the company,
the app stops working. Not fixed.
You should use a dedicated service account