Andy, it seems you've got a connection problem and hence you can't 'get out'.
On the lower right is your Systray. on it should be either a set of bars or what looks like a monitor or two. Right mouse button on this and go to NETWORK AND SHARING center. What do it say? Private network or something else? Then the CHANGE ADAPTER SETTINGS, how many are there? Any disabled? Any showing that there are connections available?
I suspect you are wireless and for some reason your connection data isn't being saved? That is really what the Yellow Triangle says and "Additional login information may be required" really means... either it has NOT saved your password or some setting is wrong, SSID, encryption, etc. Probably the reason a restore works is that it requires that information to be entered when you first install and it sees a network connection.
Confirm that this is the case and what you see please?
Normally you'd be able to connect again via that icon on the lower right with the yellow triangle. Hover over it and you should see connections available. Click on that and enter the correct info and you show connect and it should SAVE that data (may need to check a box).
If this doesn't happen, what is your network device, a USB device or on-board device?