IE 10 refuses to download file

Symptoms:

• Download history (CTRL+J) does not work
• Downloading any file does not show the download prompt (Open/Save)
• Clearing Download history using the CTRL+SHIFT+DEL menu does not help
• Recent update to IE 10

Then try deleting C:\Users\Roman\AppData\Local\Microsoft\Windows\Temporary Internet Files\counters.dat

Internet Explorer was trying to open this file with ACCES_DENIED result. Found using SysInternals Process Monitor.