The account your service is running under needs to have permission to connect to SQL Server. You can either give explicit permission to this account, or change the account the service runs under to one that has access, or use SQL authentication instead of Windows Authentication.

1) I have used the Default Service Account using SQL Server Authentication (building userid and pwd in connect string).

2) I have set the service to use my normal development account which is an Admin and then used windows auth in the connect string.
3) I have set the service to use my normal development account as in 1

All failed to connect and more importantly SQLConnect() hangs instead of erroring out with a return value.