I had the same symptoms with two installation: WordPress 3.5.1 on Windows Server-2003 with IIS6 and another one on Windows Server 2008 with IIS7.
Setting up Write & Modify permissions for “IUSR_serverhostname” (or just “IIS_IUSR” in IIS7) to your Windows temp directory (default is C:\Windows\TEMP) suggested in
http://wordpress.org/support/topic/35-on-iis7-unable-to-update-plug-ins-and-themes?replies=16
worked for me.
BTW, This particular issue was reported as fixed in 3.5.1, but apparently it hasn’t been resolved.
I guess if you are not Admin on that system, or can’t contact one, you are out of luck.
It seems that using a System TEMP folder for all upload (introduced in 3.5) was a bad idea, as an ordinary user has no control over its permissions; and I’m not sure if the solution above doesn’t compromize the security.