Every time I click "Safely Remove Hardward" on Desk Top Tray to eject my external harddrive?

something is still running from it be it a program or a file that you have opened on the computer. for example a word document. you close the word document and then try to eject the disk well word may not have actually closed which will cause the disk to think that it is still open and will not let you eject. try going to task manager and make sure that stuff has closed down.

First, turn off your computer. Second, unplug the external drive's USB cable from the computer.

also,

Your system is infected, that virus prevents the system from stopping the external drive, because a file in that drive is loaded and running. or vice versa, your PC is busy infecting that external drive. have your system checked for viruses

click start then just log off... then safely remove hardware. no need to restart