Does Deadlock imply Starvation
You should first state the deadlock freedom property and the starvation freedom property more precisely.
I use the definition in the Book: The Art of Multiprocessor Programming; Section 2.2.

Freedom from Deadlock If some thread attempts to acquire the lock, then some thread (not necessarily the thread referred to in the if statement; emphasis added) will succeed in acquiring the lock.
Freedom from Starvation Every thread that attempts to acquire the lock eventually succeeds.

Note that by definition, starvation freedom implies deadlock freedom. Thus, if a mutual exclusion algorithm suffers from deadlock, it also suffers from starvation.
A direct argument is that: deadlock means that some thread attempts to acquire the lock, but no threads succeed. That is a special kind of starvation.