the datailfe, controlfile and sp parameters are obviously the defacto ways to get that infor but if the controlfile, FRA or spfile is located on ASM it will show up in the alert log at start time. Use the tac command to read from bottom of file. this will give you the last time the database was started. assuming of course you still have that info in the alert log and it hasnt been wiped/truncated/archived since last start.
cd to bdump and run following, obviously passing in your own alert log
tac alert_<sid>.log | egrep -i "db_create_file_dest|control_files|spfile" | more