you dont need to restart the webserver in case of Windows server, just recycle Application Pool (will take a blink of an eye) and you'll be good to go.
what I am wondering is, why is it taking so long for plug-in to install, that it is giving timeout error.
Just before you proceed with diagnosis, I would prefer referring you to an hour long video tutorial to learn how to properly setup Moodle on Windows Server
http://blog.academictools.org/2015/12/installing-moodle-on-microsoft-windows.html
Where you mentioned Server 2008 R2, have you not checked ISAPI and ISAPI filters? as since R2 Server 2008, PHP is handled by FastCGI so just selecting CGI in IIS options will suffice, ISAPI was used in older versions where PHP was handled by CGI that is why PHP sites were running slow in Server 2003 era.