I am assuming that this is a regular keyed electrical switch like one used to find with garage doors and some alarm systems, if so, call the LOCK SMITH!!
They have tools that will usually allow them to extract the broken key!
With the extracted part, a GOOD lock smith should be able to cut you a new key... simple, reallllllllllly simple to do, provided they have the key blank.
Next, they may actually have a replacement if they also install garage-doors or alarm systems - or they may be able to smoke a key for you (some of them have no idea about how to blind cut a key, they should, covered in every locksmith training course I've ever read).
I've done this with a few keyed-switched instruments in the lab (actually, with the tools I have in the lab, I pull the key myself and take it to them for a re-cut - but it take a lot of patience and practice to extract the key!) (that's why I have the locksmith training... never figured a chemist would need to know... I also have electrical and plumbing, go figure)
My late-Grandpa used to just pull, braze the two parts back together, and clear the key-way on the key when his would break.
-WC