Some keyboard keys are not working on login to Yosemite The problem is that every time I start my MacBook Pro 15" Early 2011, some of the (native) keyboard keys stop working. However, if I click a restart button - it is all fine.

It is definitely not a hardware issue and this did not happen on Mavericks ever.
On the Yosemite login screen, you should see the current Input Method (keyboard) icon in the upper right corner. 

If you click on the current input method, a drop-down menu will let you choose which alternate keyboard you can use. That should let you enter it in.

If your keyboard isn't listed, the dropdown menu also has an exhaustive list of other input methods, so you can select one that should let it work. 

Note: I haven't tried to change my password to use an alternate keyboard just to see if it works. Maybe for 1000+ rep... ;)

Also, it took about 5 seconds for the input method menu to drop down, so just keep at it until it drops.