Can't connect to remote computer

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I installed TeamViewer on my desktop PC (Computer #1) and on my laptop  (Computer #2) and was able to use TeamViewer to access Computer #1 from Computer #2. For the last few days, I have been unable to connect to Computer #1.

I am out of the country, so cannot physically access Computer #1. The Management Console indicates that it is online, and the Remote Control window says "Ready to connect (secure connection)."

When I click "Connect to partner," it says "Connecting" for several seconds; then the "Ready to connect" message appears again.

On Computer #2, I have tried the following: 1) logging out and logging in again; 2) rebooting the computer; 3) reinstalling TeamViewer; 4) installing an earlier version of TV. None of these have solved the issue. As noted above, I cannot try any of these solutions on Computer #1.

I need some of the files on Computer #1. How can I again get access to this computer?