Trace flag 1222 became available in SQL 2005, and is a lot easier to read than 1204.
You will want to run just trace flag 1222. Since there will be some overhead you can switch it on for with "DBCC TRACEON (1222, -1)", wait for the deadlock to reoccur - capturing information in the error log, and then switch it off . Alternatively, 1222 can be added as a startup parameter "-T1222", but this will require a restart.
SQL Profiler can capture the deadlock graph, but it does have to be running at the time of the deadlocking event. It is quite simple to configure. You can run a server side trace to limit the overhead.
Another alternative for troubleshooting deadlocks is to view the extended events deadlock graph. This is most likely already running and past deadlock events are available to you on your SQL Server.
Do a search on this site for any of the above topics. There are many articles on this site, and many helpful postings that will get you started troubleshooting deadlocks.