Can you open up Task Manager? (Ctrl-Alt-Delete and possibly clicking on some buttons depending on how the computer is setup. BTW it might actually be helpful to know what the operating system is.)
In Task Manager you should be able to see what programs are running after clicking on something - when you open an .exe file, what program does it say is running? I'd try to get System Restore happening first but perhaps if you uninstall that program, you will be prompted as to what program should be used to open a file.
(BTW - if you right click on a text file, is there on option to Open With? If so, does it list other word processing applications? Can you open a text file in one of those applications? If so, try using the Choose Program option to reset the application used to open that file extension type - although I would still try to get System Restore to work before messing around too much with that.)
Under the File menu in Task Manager try the New Task (Run...) option - it might let you start an .exe file. Try just starting a command prompt with one of the following:
[div style="margin-left:2em; font-family:monospace;"]cmd.exe
C:\Windows\System32\cmd.exe
%systemroot%\system32\cmd.exe
If that does bring up a command prompt window, you might be able to start System Restore from there. Or if that doesn't work you can try rebooting in Safe Mode With Command Prompt as discussed here (for XP):
If your computer won't boot Windows normally and won't boot into the Safe Mode GUI, you can still access System Restore. Start by booting the system using the Safe Mode With Command Prompt option. After you log on, type the following command line at the command prompt:
[div style="margin-left:2em; font-family:monospace;"]%systemroot%\system32\restore\rstrui.exe
Press [Enter], and System Restore will run as it normally does. You can follow the steps in the wizard to perform a restore operation.[font style="font-size:0.8462em;"]
http://www.techrepublic.com/article/10-things-you-should-know-about-windows-xps-system-restore-tool/6048545[/font]
Safe Mode won't alter any user files and System Restore should not alter any user files - definitely not if they are in the My Documents folder - most probably not elsewhere except possibly the Desktop.
As far as retrieving content, you could try just copying files to a USB stick - it seems like Windows Explorer is letting you navigate, so it might also let you copy files. You can also pull the hard drive out and put it in another computer or get a USB to hard drive adaptor to allow you to transfer the files to another computer.
In fact, to be safe you may want to figure out how to backup the content and do so before trying to get the computer running again.