also is it possible to fix a broken processor pin?
Not if it's actually broken. BUT if you're lucky it may be one of the very many redundant ground pins - if it is it probably won't matter if it's broken.
You can download the pinout diagram of the CPU from this page on the Intel website
to see which pin you've broken. Look in section 4 ("Land Listing and Signal Descriptions") - pins marked "Vss" are the ground pins and you can probably run without one of them. Pins marked "Vcc" are positive power supply pins, and there's a good chance you can run without one of those as well.
Note that there is no pin at position A-1 on the pinout diagram - that should help you orient the diagram to match your CPU.