1972vet

Since this is not a connection that you use, try removing the connection that is set up for it:
Click start-->Connect To-->Show All Connections
...The Network Connections window will open. Listed there should be icons for all connection methods that are set up for your user account.

If you can Identify which of them that you use then you should be able to delete the other(s).

Be careful not to delete anything that windows created... such as "Local Area Connection". You can identify the connection you are currently using by right-clicking on the connection icon in the task bar. Select "Status" . In the Status window that opens, note the name at the top. Your connection icon in the "Network Connections" listing should be named the same.

Click start-->Control Panel-->Internet Options-->Connections
...In the Dial-Up and Virtual Private Network settings section, there should be a list showing the connection names. At least one should be listed as (default).

The connection that you use can be designated as Default. Return now to the Network Connections window. Find the icon for your connection. By right-clicking on the icon for the connection that you use, you will be presented with a menu.

The menu that opens will have the option "Set As Default". If you don't see that option in the menu, then Right-Click on the icon for the connection that IS designated as Default and select "Cancel as Default Connection"...then return to the icon for the connection that you use, right-click on it and select "Set As Default".

Close the Network Connections window. Return to the "Internet Properties" window. Near the middle of that window, select the option for Never dial a connection. Click "Apply" and "OK"...then close the Internet Properties window and reboot the system.

With this option selected, you will have to open your internet connection manually. Since designating your connection as "Default", it would now be listed in the "Show All Connections" listing. To find it, click start-->Connect To...Now the only options should be your connection icon and the "Show All Connections".

To make your connection easier to find, you can selelct "Show All Connections", Right-Click on the icon for your connection and select "Create ShortCut". Answer "Yes" to the question "Do you want to place a ShortCut on the Desktop instead". Next time you want to connect, just double-click on the icon Shortcut you placed on the Desktop.

If, by the Yahoo ToolBar you are referring to this entry:
R1 - HKCU\Software\Microsoft\Internet Explorer\SearchURL,(Default) = http://us.rd.yahoo.com/customize/yco.../www.yahoo.com
...then I should point out that it has nothing to do with a tool bar. The preference you have for your search engine that you selected in Internet Explorer is reflected by this entry. You can change that to any search engine of your choice from within Internet Explorer. In the Internet Options "Search" section, under the General tab, click the "Settings" button. Find your preference in the list and set it as Default.

For the flash player issue, did you download the uninstaller that Secunia offered you? If so, in the "Insecure" section, look for the flash player in the list. Click on the folder which will take you to the location of the offending file that should be named. Find the file inside that folder and delete it. Allow Secunia to rescan. Post back your results. Thanks!