Tom, your best bet (as Aaron said) is to check out the execution plan for the slow query in question.
Instead of running profiler for a day to see what is hitting the table I would recommend querying the plan cache for plans that hit the table.
Looking at these plans may also help guide you in your index creation.
Here is a script that could help you out:
;WITH XMLNAMESPACES(DEFAULT N'http://schemas.microsoft.com/sqlserver/2004/07/showplan')
st.text As sql_text,
CROSS APPLY sys.dm_exec_sql_text(cp.plan_handle) st
CROSS APPLY sys.dm_exec_query_plan(cp.plan_handle) qp
qp.query_plan.exist(N'//RelOp/OutputList/ColumnReference[@Table = "[TABLENAME]"]') = 1
Just replace TABLENAME (leave the square braces) with the name of the table in question. This will show you the query that was executed, and the plan, but only for those plans related to the table in question.
Granted, this is only an option if you have not recently cleared the cache, either explicitly so, or by restarting the server or SQL Server service.