How do you get a left clicker -just the plastic bit on top- to go back onto your Compaq CQ45 laptop?

If you still have all of the pieces and they are undamaged, you can replace the button by removing the protective plate surrounding the touchpad and keyboard [disassembly instructions can be obtained from HP website]. This will require removing the monitor and a bunch of other parts. Instead, I recommend buying a small usb mouse. They can be as cheap as $5.

In the meantime, you can use the tab button, shift+tab, and arrow keys to scroll through clickable items, and hit enter to "left-click" selected item. There is also an open-souce (free) program called AutoHotKey that you can install that will allow you to reassign the missing key to a button or combination of buttons on your keyboard.