Is there a train from Venice to Athens?
Yes. It will take between 37 and 41 hours.
Use this website and see what's available on your travel dates. Use 'Venise' and 'Athenes'.
Incidentally, you could make some wonderful stops as the train will go through Slovenia, Croatia, Serbia- consider taking a few days to explore these wonderful countries.
It is a very long and out-of-way route, but can be done. If you have several days and want a stop along the way, it may be a great adventure, but not the choice of most travellers and probably not covered by a rail pass if that was your thoughts. The traditional route is a ferry, and while some leave from Venice, a Train down to Ancona or Bari to catch one would be more common, arriving in Patras followed by bus or train to Athens. This cuts the travel time to about 24 hours, maybe a little more. The current best way is a budget flight, not very romantic, but then an overnight train(s) and ferries really are not either. Aegean Air flies Venice to Athens Directly, not sure what their rates will be, but 100 to 150 euro each way would be a decent guess, and would get you there in a morning as oppossed to 1 or 2 days.