Hi m4a1.
Not sure if this is a PL/SQL Developer or Windows 7 problem/bug, but is something I have come across and I believe is undependent of the specific PL/SQL Developer version/build - was using v7.1.5.1398 build.

To make your developer working go through following steps:
1. Open control panel
2. Open "User Accounts" element
3. Open "Change User Account Control Settings" element
4. In the opened window put the slider to the lowest position : "Never notify me when:"
If you can't modify the setting, you will have to contact your administrator to do it.

!!! Keep in mind in order for changes to take effect you will have to retart Windows (the machine).

The above steps worked for me and now I am able to log in the database(s).