Click on the tab labeled as 'Processes' from the list of other tabs displayed, and then trace down till you find out 'Windows Explorer' process enlisted in the list of currently running processes.
It will open the Task Manager all of its own accord. After the 'Run' tool box appears on the screen type in 'taskmgr.exe' command and hit 'Enter'. Firstly press the 'Windows logo key + R' to launch the 'Run' command. Many a times the background processes or tasks impedes the taskbar from functioning properly, thus setting the taskbar right would automatically resolve your issue with the icons. The method is one of the simples of all, yet it is very effective in bringing icons back to taskbar in case of hurry. Part 1: Fix Icon Not Showing on Taskbar by Windows Explorer