Start without key or with broken key (3-4)
I believe the answer is:
hot-wire
'start' is the definition.
(hot-wiring is a kind of starting)
'or with broken key' is the wordplay.
'broken' indicates an anagram.
'key' becomes 'e' (a musical key).
'or'+'with'='orwith'
'orwith' with letters rearranged gives 'hotwir'.
'hotwir'+'e'='HOT-WIRE'
'without key' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Another definition for hot-wire that I've seen is " Make unorthodox start".)