Part of your question (Another connection) can be solved by enabling the Security Logs. To do this you have to turn on Auditing.
The audit log appears in the Security log in Event Viewer. To enable this feature:
Click Start, click Control Panel, click Performance and Maintenance, and then click Administrative Tools.
Double-click Local Security Policy.
In the left pane, double-click Local Policies to expand it.
In the left pane, click Audit Policy to display the individual policy settings in the right pane.
Double-click Audit object access.
Select the Success check box for the security objects you want audited for successful use.
To audit unsuccessful access to these objects, select the Failure check box.
To enable auditing of both, select both check boxes.
Click OK.
The other part could be solved by looking at your Firewall log. You have to enable logging if you are using Window's Firewall.
For third party solutions have a look at Port Explorer.